Even if you do it from a browser, it is only accessible from the YouTube website run offline as a SPA.
Even then, downloaded videos can only be played for 29 days before having to reconnect most of the time, with some regions restricting it to 48 hours.
It’s not the raw video file, you can only access it from the app or website, and there’s restrictions on how long you can be offline before the app/website will stop you from watching it.
I tried to trick google by creating an account using VPN in Europe. I even managed to subscribe for Premium. Even with an active Premium subscription Youtube app won't let me use its features such as downloading, background play and picture in picture (you know, basically everything)
Because "you live in the wrong part of the world". Creating a problem, selling the solution is what they do.
Like, I don't even care about downloading, but Google intentionally cripples their mobile website experience by suppressing pip and background play. It would cost zero dollars not to do this but they did.
The fact Apple allows Google to resell their multitasking and PIP features as part of their own subscription is pretty un-Apple.