The PIP is as big a deal as you make it out to be. This is the key insight as you interview at other companies: Don’t share information that hurts you.
In the same way that you wouldn’t share your previous salary or your compensation expeditions in the interview, you also shouldn’t share past performance struggles. You don’t get points for transparency. The thinking should be that you only share information if it helps you with the job interview. In particular, you should never mention that you got PIP-ed.
Instead, use neutral phrasing like “I’m super excited about this company. I deeply resonate with the mission and people.” Or “The previous role wasn’t a good fit”