Page Branching uses Confluence’s native permission model. Branch pages inherit access from the space Branches parent page, which keeps things predictable and easy to govern: whoever can see and edit your Branches area can collaborate on branches there.
If you need branches to be visible to a smaller group, simply set page restrictions on the Branches parent or on an individual branch page, just like you would on any other Confluence page.
Branches you can’t open are not listed for you. The branch list on the original page says how many it leaves out, and if the space limits branches per page, those branches still count towards the limit.