Thanks Leonie, but sorry, that's really not a way to do, we're in 2023 .. Everybody has all photos in albums. No choice since all Apple photo apps are album based. What you are proposing it really too complicated for a so simple feature.
What I can say is it was working before IOS 16, I did it often : I just selected pictures inside synced albums on iPhone and then hide them ; however it was always impossible to hide a whole album, I was obliged to do it one photo by one, but 'select all' was available so quickly done. I can assure you it was working, at this time the Hide option was in a different place (inside share menu near Print or Store stuff).
As an expert in all programming stuff for 30 years, and iPhone user since the beginning, I would say the best (professional) way would be to tag albums as hidden on Mac Photo then iTunes sync. Then these albums would be hidden on Mac Photo and iPhone Photos (and so on with iPad, I use everything, that's why the solution must be easy if you have many devices and even more if you share your Mac Photo with many users) ; to be able to watch hidden albums, Touch Id could be used on Mac and Face Id on iPhone.
Anyway it's unbelievable that a company such as Apple dares to propose such bad tools to their customers, all their photo apps are so far from usable ... :( .. They have hundreds of certainly high level programmers, it's so incredible they cannot ask to 3 or 4 of them to improve all photos management ... :(