On Safari this can be done with Cmd+E, and it might even work on Chrome on OSX as well, but when on Windows I browse with Chrome. I do not want to type out what I want to search every time.
By search i mean search on the page, not search the internet.
If there is no built in key binding, then I hope someone can suggest a plugin or Tampermonkey style script to do it (I know that is definitely going to be possible).
Well, you can always copy it to the clipboard and paste it in the searchbox like so:
Ctrl+C, Ctrl+F, Ctrl+V
Ask and ye shall receive.
When I saw your question, I too figured it would be simple, even trivial, to throw something together to do this. Unfortunately it turned out to be much harder to do because of numerous obstacles and limitations (you can see a list of problems encountered and references in the script).
After much research, experimentation, and testing, I managed to create a Chrome userscript that can do what you want. One limitation is that it does not use the browser’s actual search/find control because the devs have not provided any programmatic access to it. However, the DOM does provide a way to search the page for specified text and jump around to them, so it does work more or less.
I enhanced it a bit so that it doesn’t trigger incorrectly:
The Find Selected userscript.
Just select the text, then click and drag it into the search bar. You can also right-click on selected text and choose "search for selected text on default search engine".
