None of the above. No one pronounces "aw" like the a in Apple. And most people do dinstinguish between "a" and "aw" by pronouncing the latter more like the a in "awe".
A dog limps into a bar. The barman looks at him and say "What can I do you for?" and
the dog replies "I'm a looking for the man that shot my pa"./pɑː/ — if I had to use "normal person's IPA", "pah" would be my attempt. This, to me, is the more common pronunciation. Should rhyme with "bra" … assuming you pronounce that like I do.
/pɔː/ — like "paw" or "awe". This is a region-specific dialect, to me. This appears to be the one you're familiar with.
See https://en.wikipedia.org/wiki/Help:IPA/English for a chart.
https://www.merriam-webster.com/dictionary/pa
Relevant for the US.