Thanks for merging. Could someone of the Discourse team change the topic title for this feature request, so that it not only involves Quote, but also Edit, Copy Quote and Ask AI? For example, you may change it to:
Floating buttons in Chat when selecting text (Quote, Edit, Copy Quote and Ask AI)
One more thing is that you can only select and quote from one reply at a time inside topics. In Chat it would work better if you could select and quote multiple messages at once via the floating buttons. Because chat messages are often short, and I can see that most of the time people in our team select (or share a screenshot 
) of multiple messages from Chat.
More steps to quote
In my original post I’ve shared that there are three steps to quote in Chat. There are actually four steps to quote in Chat. I forgot to add “Click on select” that you can see in step 2 right now: