Well, I was a bit mad when I typed that, so didn't go into details.
But what happened is likely a very rare combination of bugs, and google teaches me the first two are not unique to the xbox version. Bug one is a save glitch where the seamoth acts weird upon starting. The second one is being at an unfortunate spot where you can fall through the map and die. The third one is dying outside the map apparently leading to the game not being able to load my character at my pod as usual. Upon loading all of that occured within like 1/3 of a second, every time. I could not even see what happened. But I knew I was in a seamoth at a bottom when I saved, so googled what could be wrong.
Aaaand, thankfully the crisis is averted. Since I gained the knowledge, I got the idea to just spam the exit vehicle button like a madman as soon as my save was close to loading in. And after some attempts I was in time and got out of that deathloop.
All of the other issues I am experiencing are obvious, but not really detrimental (creatures stuck in walls, fish swimming in my base, sometimes parts of items being visible while I have something else equipped etc.).