I have a question regarding this. I´ve got into the beta and installed it on my laptop. No major issues so far and connected with all platforms I wanted to connect with. Then I was wondering how it works and installed it on another computer and found out I have to connect platforms again.

So the question is, is it supposed to work like this? I thought it should work like I connect platform once and it will get synced forever, so wherever I login to GOG, I will always see all my games on all platforms without making the connection again?

Can't answer specifically for Galaxy 2.0 since I haven't tried it yet. But this behaviour is kind of the same with the old client or even other clients like Steam. E.g. when I install Steam on another computer I have to set all my settings again like client language, download speed etc.

Edit:
Maybe don't think of Galaxy's feature as you'd permanently bind your other accounts to it but rather as a one time import of your other clients games.

Edit2:
But don't take my word for granted, I'm only speculating ;-)

Well, don't not exactly what gog intends, but as the current changelog states that the synchronisation between bookmarks isn't available yet, it at least points in that direction: What use is there to sync bookmarks, if they don't show all the games they are supposed to, because not all necessary connections are already in place.

But this will definately hit a technical obstacle as, for security reasons, you will have to authorize client connections on a new system.

That's because Galaxy doesn't sync your authentication data in their cloud.