There is also a native Wayland support PR on the OBS Github. But it may take a bit until it will be merged. I think it is driven by the same person who made the first plugin - so maybe that plugin makes some assumptions about that PR being merged (unsure, only can remember I had some problems compiling it some time ago). The GNOME one should be fine in case you are running a halfway recent GNOME version. For all other DEs it depends on them what they support and/or if a plugin exist for them.
I switched my GNOME Shell (desktop) from X11 to Wayland and everything seems to work other than screen capture, for which I'll be installing one of those plugins indeed. One of the suggested plugins looks cool in relying on pipewire, but I was having trouble building pipewire on my OS, and the other plugin implies using GNOME's LookingGlass tool, so I ended up reverting my desktop session to X11 for the screencast recording :-)
Looking forward to the next release carrying that Wayland PR for next times around.