Akonadi used to start automatically upon login for me but now it doesn't. ~/.local/share/akonadi/akonadi_control.error contains the following: D-Bus session bus went down - quitting. I can start Akonadi manually via the server configuration console without any errors though.

What could be the problem? I'm running the latest stable KDE version.

Akonadi will only automatically start if an application requests it's services. In this case, that errorr message is likely from when you logged out at the end of last session.

All right, then how come some app used to need Akonadi while now it doesn't? Before, upon login I used to get a message about some default address book being migrated successfully (Akonadi would start automatically right before that). I used to see that all the time. Now I don't get that message and Akonadi doesn't start. Are these two related in any way?

This is weird, because I haven't changed anything in my system except a few installed updates (which should be completely unrelated to KDE or its apps).

Unfortunately I don't know why that is the case. However, if it automatically starts without issue when you run KMail, KAddressBook, etc. then you do not need to worry about it.