I got a little busy.
Not sure what has been going on with Manjaro or whether it's just my sense of time that's been warped, but there seems to have been a longer than usual period between updates. I've been waiting for Blender 3.3 for a while as that has the new hair system in it, but Manjaro refused to update.
I found out at some point during these shenanigans that the new hair system was actually in 3.2 which is the version the Manjaro repo is stuck on, but wasn't appearing for me
I finally got it to do a system update by force-refreshing the mirrors, but still don't know if that did it or if an update was coming out then anyway.
Either way it didn't matter because the app that I desperately wanted to update didn't get updated. So I caved and got the snap version working.