Experiencing the same problem with Firefox 96.0.3 on Sway 1.7; I force-enabled webrender and wayland for Firefox as well.
I used to rearrange tabs by dragging them with the mouse quite often. Every time I try to do that now, it results in a hang. I can't say for sure when it started, but it's started in the past few weeks; I upgraded to 96 on Jan 11th, and have been updating the minor versions since; the 96 version upgrade is likely to blame.
More than happy to provide more details if this is hard to reproduce. I'm even willing to jump on a call and screenshare to help debug this :)