It was announced that the new URL system (@ handle) would be implemented on 10 Oct 2022.. As of November 14, 2022, the following URL formats have been discontinued:
/user
/c
/directusername

Codex is right that there is no easy way to get someone's legacy /user/ anymore. The only thing that comes back in the official API are the newer custom channel @'s. The username url still exists and is usable for old accounts that have one, but its legacy and you can't change it. As for when it became legacy, I can't find a solid date but see references to it as being legacy at least >10 years ago.

The only way to get that legacy url would be to manually search the internet & archive.org and hope that it was archived or shared somewhere.

https://support.google.com/youtube/answer/6180214?hl=en