Hi Pilot Participant, 

We have identify that record type assignments are not captured by Permission Set Group. This means, if you have record type access added in a Permission Set that belongs to a group, the group, at the moment, does not recognize the record type access and users assigned to the group will not get the record type access. We have acknowledge this bug and will look into fixing it. Will give an update when this is fixed.

Thanks to @Jan Martin who gave us feedback on this and help us reproduce the issue!