That was not my experience, and certainly not the experience of my coworkers that have been at Amazon "many, many years". If you are cozy with the people of the team you hope to get into, then is easy, otherwise, you get your CRs reviewed, asked for design docs, and need to talk with several people on the team. If you worked on a small project for a year, or were hired to maintain something that was already there, you don't get to have design docs, nor impact opportunities (even if you asked your manager for it during 1on1s). Also the next manager can make you apply (your current manager gets notified) and then rejects you, just because, and you will be in a delicate situation.
I agree - you get code reviews reviewed by the other team, design documents, and other artifacts. What I was saying was that there’s no formal interview loop like the one when you join the company. You’re not going to grow through LP questions and white boarding code.