If you select the emoji, and only the emoji, the quote will strip out the link, which is indeed not expected.
If you select any additional character, even the empty space before, the link will be selected along with the emoji.
However, this issue has nothing to do with the full quote button, so I advise creating a Contribute > Bug topic for this, but I’m not sure resources will be allocated to fix such an edge case, or with a pr-welcome maybe. 