This is slightly embarassing, but it turns out that GOG Galaxy had decided not to install the DLC after it said that it was installed.
For future reference, installed PoE 2 DLC packages have a dirty great big tick next to them on the main menu screen, while available ones are in grey.
And in in case anyone was wondering, I'm pretty sure the extra drinks added by the Rum Runner's DLC are available in the tavern that used to be a ship in Dunnage.