I just died in my ship out in space to hostile ships, and now I'm stuck in a respawn/death loop where the game respawns me in some planet's atmosphere from which I fall to my death and then respawn in the same planet's atmosphere to die all over again. I thought force-quitting and re-entering the game would help, but it made no difference. I'm not sure what is supposed to happen, but I strongly suspect it's not this. What can I do to get out of this?

You can try to load your latest manual save. If that doesn't work restore the saves from a recent backup which you surely have ;)

In case you dont have a proper manual save to reload from, or do not want to lose any progress from when u made it till ur last autosave, you could also try to join one of your friends either via GoG Galaxy join button or by selecting multiplayer from the main menu of the game.

Upon joining you should spawn in space, inside your spaceship, in the system where the friend whom you joined is. You can continue playing from there, though i dont know where you will spawn next time you play in single-player, since position is not saved in multiplayer. I would suggest exiting the group after joining and saving inside the Anomaly, your Freighter or a Space Station.

If all else fails, perhaps you may be able to manually change your spawn location using the save editor.