Even after the last update, some players still had difficulties with the Steam Achievements. Unfortunately, fixing the Overlay, did not resolve the issue.
After some research and even more tinkering with the Steamworks.NET framework, I might have found a solution. Forcing a callback function when triggering achievements appears to solve this problem according to the Unity forum.
Again, I apologize for the delay and really hope it works this time!
Steam API Bugfix
Some players appear to have difficulties with the Steam Achievements as well as the Steam Overlay.
After some tinkering with the Steamworks.NET framework, I made sure that the Steam Overlay works even if the game is started directly from the .exe-file or in offline mode.
Hopefully, this also resolves the issues with the Steam Achievements. Unfortunately, I cannot playtest this, as the problem only occurs rarely on certain devices.
Sorry for the delay and the troubles! And thanks to the people spotting this error and helping me (hopefully) fix it.