The video files do live on servers. Paid servers like satellite.earth store your files for as long as you pay them too. You can host videos up to 1gb with them. Whereas free servers have a file size limit that's much lower and no guarantee they'll keep your files. For instance, the default blossom server software will delete your files two weeks after the last time someone looked at them.

For a casual user, free servers are fine. If you're a prolific poster, you'd be better off using a paid service.