Yes almost all power meters should work with a 510. My stages worked fine with my 800 I had up until a couple months ago. I think PM for MTB isn’t super useful during the ride unless you have some long steadyish climbs so that you can pace yourself.
But if you are racing then the post race analysis can be useful. E.g. if someone attacks and you couldn’t follow then you can go back and see what the power and duration was that you weren’t able to stick with. It will also be able to give you TSS numbers so that you can better track your overall training load.
But I do all of my indoor training on a dumb trainer with a stages PM and other than noise and convenience I don’t see a reason to upgrade to a smart trainer unless the trainer dies. Sure it’s a bit annoying to have to swap wheels to go from indoor to outdoor riding but it’s and extra 30-60 seconds. That time savings isn’t worth $500 to me.