XTRMNTR2K: Alright, my issue is finally resolved! Here's what happened:
As instructed, I added a free item to my library via Galaxy (Shadow Warrior Classic Complete). However, after doing so, nothing changed. It did not trigger the refresh of the database.
After quitting Galaxy and running it again later, I decided to try adding another free item (The Silver Case Demo). And lo and behold, while looking at my available Deadfire DLC, the Rum Runners Pack suddenly appears out of thin air! :D
So, for everyone affected by this issue, try adding a few (free) items to your GOG library from within Galaxy, it may trigger the needed refresh of the database and fix your problem. :)
This worked for me as well! After I added the free game I was able to click "Install" for the Rum package, rather than just having a "Buy" button. Thanks! :)