I met a professor who I had contacted through email in person. We sat down once and chatted about his work. I I was doing research through a program which payed half of my stipend and expected Princeton to pay the other half. Since I came from a pretty prestigious university, it was pretty much assumed that I was qualified for the job. The interview was more of a get to know each other.

Very standard for postdoc application. Cold email PI, provide references, a zoom call or two, flown out to give a 1 hr talk and chat with other members of the team. Total interview about 1.5-2 days. note: interview difficulty marked as "average" for a postdoc interview, but it is "very easy" compared to industry interviews