Domestically I've seen both - where Group 1 is called on its own, and where both Groups 1 and 2 are called simultaneously. Perhaps it's dependent on loads (or if they're running late) - if there are only a few P1/WP flying Y they might call Group 2 at the same time to speed up boarding?
Internationally, QF have created a Priority Group 1ST (First) for F pax, so that the priority group orders go:
- 1ST (First) - For F pax only
- Priority Group 1 - For J pax and P1/WP/OWE
- Priority Group 2 - For SG/OWS
See:
https://www.qantas.com/au/en/travel-info/boarding.html ("Will Priority Boarding still be Available?")
(Not confusing at all!)
While priority boarding is a OWE benefit I don't think that means necessarily boarding with F pax. While BA and CX do, AA don't - they put OWE in group 2 (behind ConciergeKey, First, Business, Families and AA Executive Platinum).