So after deciding to try out SPT-AKI again after a few months, I did my usual. Trawl through the new mods section and download any that piequed my interest. Dragged them all into AKI's mods folder, configured them (hopefully) correctly, launched the server, launched the game. Created and named a new PMC, started inspecting everything.
All was well.
Then I accepted Prapor's first task: Debut, and noticed that the little spinning loading symbol was stuck in the bottom right corner of my screen, and then I noticed that everything was stuck. I couldn't accept anymore tasks, couldn't move anything to and from the stash, trader inventories wouldn't load etc. So I closed the game, reopened it, same thing happened again on accepting Therapist's first task. Closed the game again, and then pressed log-out on the launcher, and noticed that it wasn't connecting to the server.
Took a look at the server log, nothing seemed out of the ordinary error-wise to my untrained eyes. Took a look at the client log, and noticed that there was indeed a big error. That was as far as my own (poor) troubleshooting attempt went.