Most of what you describe is external to TUF (authenticating, logging, the specifics of the data you're protecting and how you transfer it once it's validated).

A couple things you pointed out are definitely hard with TUF right now:

> For instance, administrator approving registration is not a single person, but group of administrators, each with different permissions on streams

TUF is being actively developed and this type of approval pattern is planned: https://github.com/theupdateframework/tuf/issues/346

> Client cannot download stream of some other client, and cannot get any information on overlays used by other clients, etc.

This is currently a limitation of TUF, but it is known and there are some tentative plans to address it. If you have specific use cases you'd like to contribute to the discussion, there are GitHub issues and the mailing list.

I think it's worth pointing out that even if you don't use TUF, you need to be thinking about the vulnerabilities it's designed to protect against. Once you start doing that you'll probably end up with something similar modulo formats and transport.