It turns out that the cathedral grounds used to contain the entrance to an old crypt. It's sealed off now, but the rumours attracted some thieves – one tried to get inside via a dried-up well. Bad idea. Still, I learnt that the entrance is hidden in the cathedral courtyard under a memorial stone marked with St. Mihai's personal sigil.
The XP shown is the base quest reward; other bonuses or rewards earned earlier are separate.