I have not booked Star Alliance flights on an 016 ticket for a number of years. It used to be easy and then it got expensive booking 016 tickets with no UA flights on them. I book directly with Star Alliance carriers and input my UA FF# at time of booking. I recognize PQP is capped and the PQP earned is often less than I spend on the flight but I would rather save cash.

Not sure that adrldresses your issue but if you want the low TAP fare book on the TAP website.

Edit: Try Google flights and see if UA is one of the ticket options. It probably will not be a choice if no UA flights involved.