Scenarios:

I lived overseas for a while so I rented my primary residence during my absence.

I have a passive loss carryover in year 1. I had additional passive loss carryover in year 2. The house became my primary residence in year 3.

Can I claim my passive loss carryover in year 3 against regular(active) income? Or do I just lose the passive loss unless I have a rental income again in my lifetime?

You either have to wait until you show a rental income while you own the house, or until you sell the property, before you can claim the passive loss carryover as a deduction.