Here's what I found:
In this script:
https://docs.google.com/static/spreadsheets2/client/js/1150385833-codemirror.js
I found this function:
function onCopyCut(e) {
  if (!belongsToInput(e) || signalDOMEvent(cm, e))
    return;
  if (cm.somethingSelected()) {
    setLastCopied({
      lineWise: false,
      text: cm.getSelections()
    });
    if (e.type == "cut")
      cm.replaceSelection("", null, "cut")
  } else if (!cm.options.lineWiseCopyCut)
    return;
  else {
    var ranges = copyableRanges(cm);
    setLastCopied({
      lineWise: true,
      text: ranges.text
    });
    if (e.type == "cut")
      cm.operation(function() {
        cm.setSelections(ranges.ranges, 0, sel_dontScroll);
        cm.replaceSelection("", null, "cut")
      })
  }
  if (e.clipboardData) {
    e.clipboardData.clearData();
    var content = lastCopied.text.join("\n");
    e.clipboardData.setData("Text", content);
    if (e.clipboardData.getData("Text") == content) {
      e.preventDefault();
      return
    }
  }
  var kludge = hiddenTextarea(),
    te = kludge.firstChild;
  cm.display.lineSpace.insertBefore(kludge, cm.display.lineSpace.firstChild);
  te.value = lastCopied.text.join("\n");
  var hadFocus = document.activeElement;
  selectInput(te);
  setTimeout(function() {
    cm.display.lineSpace.removeChild(kludge);
    hadFocus.focus();
    if (hadFocus == div)
      input.showPrimarySelection()
  }, 50)
}
NEW FIND
I found that Google sheets loads this script:
(function() {
    window._docs_chrome_extension_exists = !0;
    window._docs_chrome_extension_features_version = 1;
    window._docs_chrome_extension_permissions = "alarms clipboardRead clipboardWrite identity power storage unlimitedStorage".split(" ");
}
).call(this);
This is tied to their own extensions
NEW FIND 2
When I paste in a cell, it uses these two functions:
Script: https://docs.google.com/static/spreadsheets2/client/js/1526657789-waffle_js_prod_core.js
p.B_a = function(a) {
  var b = a.Ge().clipboardData;
  if (b && (b = b.getData("text/plain"),
      !be(Kf(b)))) {
    b = Lm(b);
    var c = this.C.getRange(),
      d = this.C.getRange();
    d.jq() && $fc(this.Fd(), d) == this.getValue().length && (c = this.Fd(),
      d = c.childNodes.length,
      c = TJ(c, 0 < d && XJ(c.lastChild) ? d - 1 : d));
    c.yP(b);
    VJ(b, !1);
    a.preventDefault()
  }
};
p.Z1b = function() {
  var a = this.C.getRange();
  a && 1 < fec(a).textContent.length && SAc(this)
}
NEW FIND 3
This function is used when I select all and copy:
Script: https://docs.google.com/static/spreadsheets2/client/js/1526657789-waffle_js_prod_core.js
p.bxa = function(a, b) {
  this.D = b && b.Ge().clipboardData || null;
  this.J = !1;
  try {
    this.rda();
    if (this.D && "paste" == b.type) {
      var c = this.D,
        d = this.L,
        e = {},
        f = [];
      if (void 0 !== c.items)
        for (var h = c.items, k = 0; k < h.length; k++) {
          var l = h[k],
            n = l.type;
          f.push(n);
          if (!e[n] && d(n)) {
            a: switch (l.kind) {
              case "string":
                var q = xk(c.getData(l.type));
                break a;
              case "file":
                var t = l.getAsFile();
                q = t ? Bnd(t) : null;
                break a;
              default:
                q = null
            }
            var u = q;
            u && (e[n] = u)
          }
        }
      else {
        var z = c.types || [];
        for (h = 0; h < z.length; h++) {
          var E = z[h];
          f.push(E);
          !e[E] && d(E) && (e[E] = xk(c.getData(E)))
        }
        k = c.files || [];
        for (c = 0; c < k.length; c++) {
          u = k[c];
          var L = u.type;
          f.push(L);
          !e[L] && d(L) && (e[L] = Bnd(u))
        }
      }
      this.C = e;
      a: {
        for (d = 0; d < f.length; d++)
          if ("text/html" == f[d]) {
            var Q = !0;
            break a
          }
        Q = !1
      }
      this.H = Q || !And(f)
    }
    this.F.bxa(a, b);
    this.J && b.preventDefault()
  } finally {
    this.D = null
  }
}
ANSWER TO YOUR COMMENT
Here is the difference between e.clipboardData.setData() and execCommand("copy"):
e.clipboardData.setData() is used to manipulate the data going to the clipboard.
execCommand("copy") programatically calls the CMD/CTRL + C.
If you call execCommand("copy"), it will just copy your current selection just as if you pressed CMD/CTRL + C.  You can also use this function with e.clipboardData.setData():
//Button being a HTML button element
button.addEventListener("click",function(){
  execCommand("copy");
});
//This function is called by a click or CMD/CTRL + C
window.addEventListener("copy",function(e){
  e.preventDefault();  
  e.clipboardData.setData("text/plain", "Hey!");
}
NEW FIND 3 (POSSIBLE ANSWER)
Don't use setTimeout for simulating long text because it will freeze up the UI.  Instead, just use a large chunk of text.
This script works without timing out.
window.addEventListener('copy', function(e) {
  e.preventDefault();
  console.log("Started!");
  //This will throw an error on StackOverflow, but works on my website.
  //Use this to disable it for testing on StackOverflow
  //if (!(navigator.clipboard)) {
  if (navigator.clipboard) {
    document.getElementById("status").innerHTML = 'Copying, do not leave page.';
    document.getElementById("main").style.backgroundColor = '#BB595C';
    tryCopyAsync(e).then(() =>
      document.getElementById("main").style.backgroundColor = '#59BBB7',
      document.getElementById("status").innerHTML = 'Idle... Try copying',
      console.log('Copied!')
    );
  } else {
    console.log('Not async...');
    tryCopy(e);
    console.log('Copied!');
  }
});
function tryCopy(e) {
  e.clipboardData.setData("text/html", getText());
}
function getText() {
  var html = '';
  var row = '<div></div>';
  for (i = 0; i < 1000000; i++) {
    html += row;
  }
  return html;
}
async function tryCopyAsync(e) {
  navigator.clipboard.writeText(await getTextAsync());
}
async function getTextAsync() {
  var html = '';
  var row = '<div></div>';
  await waitNextFrame();
  for (i = 0; i < 1000000; i++) {
    html += row;
  }
  await waitNextFrame();
  html = [new ClipboardItem({"text/html": new Blob([html], {type: 'text/html'})})];
  return html;
}
//Credit: https://stackoverflow.com/a/66165276/7872728
function waitNextFrame() {
  return new Promise(postTask);
}
function postTask(task) {
  const channel = postTask.channel || new MessageChannel();
  channel.port1.addEventListener("message", () => task(), {
    once: true
  });
  channel.port2.postMessage("");
  channel.port1.start();
}
#main{
  width:100%;
  height:100vh;
  background:gray;
  color:white;
  font-weight:bold;
}
#status{
  text-align:center;
  padding-top:24px;
  font-size:16pt;
}
body{
  padding:0;
  margin:0;
  overflow:hidden;
}
<div id='main'>
  <div id='status'>Idle... Try copying</div>
</div>
 
 
To test, make sure you click inside the snippet before copying.
Full DEMO
window.addEventListener("load", function() {
  window.addEventListener("click", function() {
    hideCopying();
  });
  fallbackCopy = 0;
  if (navigator.permissions && navigator.permissions.query && notUnsupportedBrowser()) {
    navigator.permissions.query({
      name: 'clipboard-write'
    }).then(function(result) {
      if (result.state === 'granted') {
        clipboardAccess = 1;
      } else if (result.state === 'prompt') {
        clipboardAccess = 2;
      } else {
        clipboardAccess = 0;
      }
    });
  } else {
    clipboardAccess = 0;
  }
  window.addEventListener('copy', function(e) {
    if (fallbackCopy === 0) {
      showCopying();
      console.log("Started!");
      if (clipboardAccess > 0) {
        e.preventDefault();
        showCopying();
        tryCopyAsync(e).then(() =>
          hideCopying(),
          console.log('Copied! (Async)')
        );
      } else if (e.clipboardData) {
        e.preventDefault();
        console.log('Not async...');
        try {
          showCopying();
          tryCopy(e);
          console.log('Copied! (Not async)');
          hideCopying();
        } catch (error) {
          console.log(error.message);
        }
      } else {
        console.log('Not async fallback...');
        try {
          tryCopyFallback();
          console.log('Copied! (Fallback)');
        } catch (error) {
          console.log(error.message);
        }
        hideCopying();
      }
    } else {
      fallbackCopy = 0;
    }
  });
});
function notUnsupportedBrowser() {
  if (typeof InstallTrigger !== 'undefined') {
    return false;
  } else {
    return true;
  }
}
function tryCopyFallback() {
  var copyEl = document.createElement
  var body = document.body;
  var input = document.createElement("textarea");
  var text = getText();
  input.setAttribute('readonly', '');
  input.style.position = 'absolute';
  input.style.top = '-10000px';
  input.style.left = '-10000px';
  input.innerHTML = text;
  body.appendChild(input);
  input.focus();
  input.select();
  fallbackCopy = 1;
  document.execCommand("copy");
}
function hideCopying() {
  el("main").style.backgroundColor = '#59BBB7';
  el("status").innerHTML = 'Idle... Try copying';
}
function showCopying() {
  el("status").innerHTML = 'Copying, do not leave page.';
  el("main").style.backgroundColor = '#BB595C';
}
function el(a) {
  return document.getElementById(a);
}
function tryCopy(e) {
  e.clipboardData.setData("text/html", getText());
  e.clipboardData.setData("text/plain", getText());
}
function getText() {
  var html = '';
  var row = '<div></div>';
  for (i = 0; i < 1000000; i++) {
    html += row;
  }
  return html;
}
async function tryCopyAsync(e) {
  navigator.clipboard.write(await getTextAsync());
}
async function getTextAsync() {
  var html = '';
  var row = '<div></div>';
  await waitNextFrame();
  for (i = 0; i < 1000000; i++) {
    html += row;
  }
  await waitNextFrame();
  html = [new ClipboardItem({"text/html": new Blob([html], {type: 'text/html'}),"text/plain": new Blob([html], {type: 'text/plain'})})];
  return html;
}
//Credit: https://stackoverflow.com/a/66165276/7872728
function waitNextFrame() {
  return new Promise(postTask);
}
function postTask(task) {
  const channel = postTask.channel || new MessageChannel();
  channel.port1.addEventListener("message", () => task(), {
    once: true
  });
  channel.port2.postMessage("");
  channel.port1.start();
}
#main {
  width: 500px;
  height: 200px;
  background: gray;
  background: rgba(0, 0, 0, 0.4);
  color: white;
  font-weight: bold;
  margin-left: calc(50% - 250px);
  margin-top: calc(50vh - 100px);
  border-radius: 12px;
  border: 3px solid #fff;
  border: 3px solid rgba(0, 0, 0, 0.4);
  box-shadow: 5px 5px 50px -15px #000;
  box-shadow: 20px 20px 50px 15px rgba(0, 0, 0, 0.3);
}
#status {
  text-align: center;
  line-height: 180px;
  vertical-align: middle;
  font-size: 16pt;
}
body {
  background: lightgrey;
  background: linear-gradient(325deg, rgba(81, 158, 155, 1) 0%, rgba(157, 76, 79, 1) 100%);
  font-family: arial;
  height: 100vh;
  padding: 0;
  margin: 0;
  overflow: hidden;
}
@media only screen and (max-width: 700px) {
  #main {
    width: 100%;
    height: 100vh;
    border: 0;
    border-radius: 0;
    margin: 0;
  }
  #status {
    line-height: calc(100vh - 20px);
  }
}
<!DOCTYPE html>
<html>
  <head>
    <title>Clipboard Test</title>
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <meta charset='UTF-8'>
  </head>
  <body>
    <div id='main'>
      <div id='status'>Click the webpage to start.</div>
    </div>
  </body>
</html>
 
 
DEMO webpage: Here is my DEMO
HELPFUL LINKS