You can have every version of ArchiCAD ever created and it will not cause a BIM Server or other problem.
Since you say you were testing BS for the first time, I assume that you did not install the BS for 13 or 14? If you did, but just never used them, then you might uninstall those. (Not ArchiCAD, just the BIM Servers for 13/14.)
There were no reports such as yours during beta and pre-release testing. Because adding the 14 module to your BS allowed a friend to access things, the problem appears to me to be with your user account, not with the BS.
Sounds like you have already run a full repair permissions on your laptop and a disk repair (from a bootable CD)? If so, then try creating a fresh user account on your laptop and see if you can access the shared project from that account.
Karl
One of the forum moderators
AC 28 USA and earlier • macOS Sequoia 15.2, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB