For me on my android device and my iPad it appears to be working. Never had any issues on the desktop browsers. S
The issues on touch devices is wrapped up in the context menu that appears when you select text. That control does not release until its is done, at which point it collapses the text selection, which causes subsequent functions/events to see an empty selection.
Android allows us to catch a contextmenu event so our button is inside, or part of, that control which allows use to capture the text as a quote. We also need to be in there to get the button to appear at all.
iPad, really iOS > 13.1, shut off the contextmenu eventso even though the quote button does show up, when you clicked on it, remember it is outside the contextmenu, it was like clicking elsewhere on the page, the text selection collapses and quick quote saw nothing. I moved this to an earlier event in the touch/point/click stack and that seems to allow us to grab the selected text before the built in contextmenu has time to clear it.
If you are thinking all that sounds like a PITA, then good you do understand what I typed
@radu81 check if this new version works for you.
Also on your mobile device, could you post what the output of this page is: http://output.jsbin.com/urowoh I entered your device details and pixel density in an emulator and the site layout looks good, but what you posted looks like what I get on a very narrow screen.