In Firefox for Android, the two different menus after selecting text look like this:
The green-circled part is Firefox’s action menu. The red-circled part is Discourse’s.
I selected the “Quote” menu item to start this reply with the associated quoted text, as highlighted in the image.
Thank you @gnoitall - I didn’t want to use a screenshot from my device as I have additional options (at least one is probably because I’m a mod) and wanted to reduce the confusion!
Safari on an iPhone isn’t very different. Sometimes the menus overlap and get in each other’s way, and you have to try a few times. Also, the browser menu will sometimes appear without the Discourse menu. Again, just try a couple times and it eventually works.