Tracking version may seem unnecessary, but sometimes there are major changes to the way an emulator works or performs. In cases like that, knowing which version a run was performed on may be necessary for adjustments or additional restrictions.

As far as allowed emulators go, both Xebra and Bizhawk work just fine for me, and Bizhawk is still an extremely popular emulator. I've never really played around with Mednafen so I can't really speak to it, other than that I believe one of the PSX Cores in Bizhawk is based off of it.

I agree that DuckStation is likely going to be the preferred emulator going forward by runners though.