One of the most asked questions here and on reddit is traveling on AP while your AOS is pending. Yes, you can use it to travel without a question but there is always an element of risk that you should be prepared in the event that things go sour. The ultimate discretion to let you back in rests on the CBP Officer you get that day. It depends on who you get and if they have not had their coffee, are having a bad day or if the officer is simply just a jerk. I got the latter.
I traveled back home to Canada for 1 week. On Friday, 8/26 at around 1pm, the CBP agent in Halifax was very belligerent and tried a "gotcha" approach. He said "so you entered the US on B2 after getting married and adjusted status in the US to beat the system, didn't you?". I was very calm and politely said no. He kept accusing me hoping that I would bend. He said "why did you not wait in Canada to apply" and he kept saying "I knew you wanted to cheat the system". At that point, I lost my cool and the only thing that I kept saying repeatedly to the jerk 5 different times after another 5 accusatory questions was "That's not what happened and I can prove it" over and over again. Towards the end, I stopped answering his questions and just looked at him in disbelief from those questions (Side note: I have copies in my computer showing that I never intended to adjust status from B2 as we were locked out of COVID. I had proof that when I entered on B2, it was supposed to be temporary. We had a return ticket and we only sold our house in Canada 1 year after I adjusted). I was very confident about my case so I responded in kind to the belligerent officer. He never asked for proof. He just wanted to rile me up which he did and gave up.
When his attempt to frame me was unsuccessful, he finally sent me to Secondary Passport Control where I just waited for 30 minutes to be processed. As I was waiting in Secondary, I reflected that the way I handled the first belligerent CBP officer could have gone bad. The rude CBP Officer could have denied me entry even though I thought at that time that I had a strong case. The lady at the Secondary called my name and was very nice. She did not ask any question. She stamped my passport and told me that the stamp is valid for 1 year.
Would I travel with my AP again? The answer is NO if I can help it. This is just my experience. I am a Canadian Citizen, married to USC and adjusted from B2 over a year ago still waiting for my greencard. No overstay or any other immigration issue.