Whilst I haven't tried the PS5 version of the game, the PS4 trophy list does not auto pop. What it does instead is makes every challenge appear as 99% complete, so for instance the trophy 'Angel of Death' requires 1 kill instead of 100 to unlock, and 'Where Credit is Due' requires earning 1 credit instead of 100000. Along with this, there's unobtainable trophies that you can't unlock due to events being a one-time occurrence (finding all caves in orb vallis, reaching rank 5 for vent kids/Fortuna) so this means you'll lock yourself from getting 100% trophies. This is assuming you've completed all challenges on a different platform. It might differ if you haven't completed these one-time challenges.
I've heard that the PS5 version does autopop all trophies and judging by peoples times on PSN profiles for the 100% (fastest being 6 seconds lol), it's very likely that it's working as intended.
From my experience trying this and looking for information, the issues regarding the unobtainable trophies has been an issue since the PS4 <-> PS5 changes and so far DE hasn't fully acknowledged the issue so I'm not sure if it will ever be fixed.
Same for me, other unobtainable trophies include Ride or Die, Tomb Looter, Vallis Spelunker & Race Ace. BTW Some Assembly Required is just redoing the railjack quest so that one should be fine.
