Thank you for these hints! Connection to your test setup works fine. I changed my password to a simple one (only lowercase letters), but that didn't help. I'll have to look into the other things you mentioned.

Update: In the terminal output there are "406 Not acceptable" errors from the server. With some googling I found discussions about similar problems, and now I think it's a problem with some mod_security rules on the host. Tried to edit .htaccess according to some advice given in those discussions, but no luck. I guess I'll need to contact my hosting service about this.