My PI publicly humiliated my colleague. I want to report the incident but don't have a recording. What should I do?
We do not know your local laws and culture, so beware that advice here may be inaccurate.

He makes micro-bullying or threatening statements occasionally, but this public humiliation seemed very serious and crossed a red line.


It is the pattern of behavior, not the specific example you gave, that is what you need to report.
A recording is not necessary to make a complaint.
Reports are usually made to a union, ombudsperson, office of civil rights, or diversity office.  It depends on local customs.  Check your university's policies, or possibly local laws.
Usually being rude, offensive, inappropriate, wrong, or stupid is not against the rules, but threats, bullying, and harassment are.  Do not expect all bad behavior to result in punishment.
Do expect to get the same amount of leave that the university policy
says you should get.


making judgemental statements

Keep in mind that judging people is part of the PIs job.  But it should be done in an appropriate manner.