The "Advisor Requesting an Audience" event card is stuck on my event list in Kingdom Management. I finish the meeting trigger for the Level 5 Arcane upgrade project, and then the card never disappears. I've lost hours having to go back because of bugs before, so if you have any advice on how to handle it, I welcome the help.

An for reference, I've tried loading an earlier save, and the issue is constant and recurring.

Yeah, i have something similar. I have two cards lining up there and no advisor showing up in the throne room. Some later events have this bug, that they do not have this "erase card after meeting"-line. So, you have to live with it until they fix it.
I read in some forum, that they did only do the bug checking before release for the early part of the game. This part, which runs well and makes fun. The later part on the other side....
In my case, i have deceided to wait until december, until i play again, so they have had enough time to solve all this strange bugs.