I’m not trying to be difficult but this is very easy to search and the combative tone is unnecessary. I can tell you firsthand my Xbox does it, but that doesn’t really do anything for you because you already doubt me for some reason. You should still look it up to confirm it for yourself. You can tie users to controllers and set that for login. It’s a documented, widely used feature. I get that may sound ridiculous to you but it’s been standard for years.
I don't mean to be combative, I've just genuinely never used a console with that. The perils of mostly using PCs and Nintendo ones, I guess? If it's standard with both Xbox and Sony that does cleanly explain the press any button screen, although I wonder why they leave it in for the PC ports.