As part of fish's intentional aim towards simplicity, it avoids syntactic sugar found in zsh. The equivalent to the zsh-only code <<< "to be prepended" < text.txt | sponge text.txt in fish is:
begin; echo "to be prepended"; cat test.txt; end | sponge test.txt
sponge is a tool from the moreutils package; the fish version requires it just as much as the zsh original did. However, you could replace it with a function easily enough; consider the below:
# note that this requires GNU chmod, though it works if you have it installed under a
# different name (f/e, installing "coreutils" on MacOS with nixpkgs, macports, etc),
# it tries to figure that out.
function copy_file_permissions -a srcfile destfile
  if command -v coreutils &>/dev/null  # works with Nixpkgs-installed coreutils on Mac
    coreutils --coreutils-prog=chmod --reference=$srcfile -- $destfile
  else if command -v gchmod &>/dev/null  # works w/ Homebrew coreutils on Mac
    gchmod --reference=$srcfile -- $destfile
  else
    # hope that just "chmod" is the GNU version, or --reference won't work
    chmod --reference=$srcfile -- $destfile
  end
end
function mysponge -a destname
  set tempfile (mktemp -t $destname.XXXXXX)
  if test -e $destname
    copy_file_permissions $destname $tempfile
  end
  cat >$tempfile
  mv -- $tempfile $destname
end
function prependString -a stringToPrepend outputName
  begin
    echo $stringToPrepend
    cat -- $outputName
  end | mysponge $outputName
end
prependString "First Line" out.txt
prependString "No I'm First" out.txt