I've contacted the devs about this issue. Let's see if i get an answer.
However, while we're waiting i managed to get the overlay and achievements working. This needs a rollback to version 1.028b which can be done easily with Galaxy (Manage installation, Configure, Show more versions and then select Version 1.028b. Since the new "Infiltrator Mode" has no achievements on GOG yet, this isn't a big problem.
Once you've rolled the game back to that version you can download the modified "goggame-1662585593.info", which fixes the overlay, here:
Edit: Link removed. The latest update fixed the overlay and achievements issues. :)
Exit Galaxy. (Close it completely) Extract the file into the game's installation folder and overwrite the existing one. Now move the whole installation folder to a directory where Galaxy isn't looking for your installed games (In my case i moved it to the desktop) Restart Galaxy. Then move the installation folder back to where it was before and search for the game inside Galaxy. (It'll show as not installed) Right click on the game's cover, Manage installation and Import folder. Select the game's folder and add it to Galaxy again. Now start the game. The modified file contains the latest buildID, so Galaxy won't show you an update to the latest version.
Post edited March 12, 2021 by Hustlefan