Ok, have found this:
The repair tool “Recalculate private and hidden forums” has a bug in it 🙁
When that repair tool is run private and hidden forum are assigned both _bbp_private_forums and _bbp_hidden_forums statuses so this is why a user with the Participant role could not read a private forum as after that tool had been run it was also been given the hidden status also.
The workaround for this is to do exactly what you did by “changing each forum from Private to Public back to Private” as this doesn’t touch the broken repair tool and sets the visibility status correctly.
So, “changing each forum from Private to Public back to Private” fixed my issue.
