Really? I haven’t seen that. No Captchas ever I think.
The phone number could be for the 2FA but no idea, I don’t think I have seen it, for 2FA I have the usual authenticator, that said they have my phone for sure at least for shipping but maybe I did get asked for it and I don’t remember, they have it for shipping anyway so…
But logged out… no issues there if anything it works like Facebook where not sure what they have but the session last forever…
Of course I am using my Amazon from Spain there might be differences, like just due the laws alone I expect differences on the American one.