Update: After going back and making a few other choices, I've gotten a similar error at any point in which I'm, likely, supposed to walk out of the house (to meet up with Cove).
I had to reinstall the itch app and it updated everything when I did so (I believe), then was able to purchase Baxter's DLC. I had to copy paste all the other DLCs back into the game folder, but made sure that each of them were considered installed by the front menu screen. I did start a new game, but still have bunch of old saves accessible. I was able to go back and choose the other soiree option on Cove's side, with the same game, choices made, etc, and there doesn't seem to be any issues in this particular moment. Anyway here's a screenshot of the game folder. 