How easy is it to transfer between teams? Some companies make this easy, others make it almost harder to apply internally then externally.
Most of the time its somewhere in between. You'll speak with the manager, speak with the team, you each review each other's artifacts, and if everyone's happy, you swap over. The balance of power is pretty nice. I've dropped out of the process many, many times after starting talking with management. Or even just learning more about what the team itself does (I couldn't live with myself if I worked on pre-roll ads, for example. So I noped out of that one).
Not familiar with Amazon culture so I don't know if that'd be considered acceptable behavior. I hope not!
The manager should put those bad things _in writing_ during performance reviews instead of trying to prevent their employees from leaving by dunking on them after they are informed about the fact.
And from what I understand at Amazon, it's kind of the same thing, but PIPs have been aggressively weaponized.