first of all when you say {gog version} which 1 is that? there is; Windows Galaxy, Windows offline installer and Mac ... the point is files are put in different locations and Mac systems don't play the same build which is a requirement of muliplay
next boot up the game in single player, make a new Tal and run around the starting area for a min [under the map on the top right hand side] what build number shows in the ui + does the game actually play?
assuming no red flags yet, goto game options and pick 'dirrect connect' the UNTICK 'cross saves'... make sure to apply this settings before shutting the game down
i'm going to assume Windows 10 [Lan or wifi] because W11 doesn't like games and really doesn't like wifi... open Galaxy game next to the play buttion hit the drop down down, past 'manage instelation' and pick 'show folder'****
**** if you have off line installs just goto the game installed location and if you have both then offline install is the one with ' in the title i.e, Baldur's Gate 3 instead of Baldurs Gate 3
reguardless the file you need is the - Launch Baldur's Gate 3 shortcut and it will have the ' in both versions
ok right click on it and select 'run as administrator' from the drop down list, this will fire up the Larian launcher [as admin] but without the Galaxy overlay i.e, your time played will not be tracked and you can't take screengrabs with F12 but otherwise the game runs as normal... create a new user profile and test if a new multiplayer game will let you play your mates now
p.s, this question would be easyer to answer on the gog forums because we can post images there without fucking about having to host them ourselves but if the above test works then the issue is in your system files not the network