Most of the problems below can be solved by restricting the permissions on the video. If you want to just show it to the department then add the department security group to the permission.
https://docs.microsoft.com/de-de/stream/portal-permissions
Then it does not show in trending.

I want every user be able to view - but just not show up in trending or "new"

You got my vote. We link the videos to the LMS and only want relevant videos to show.

This feature is not required. Just do this. https://youtu.be/REY-di_m8Z4

In the education context this becomes really important. Effectively you have to think of a school organisations being at least two different audiences - Staff and students. They have to be treated differently. We are talking state-wide in this deployment.

Students shouldn't see trending departmental videos. It's distracting in the teaching context and the departmental videos are targeted for internal staff use.

I suggest you disable trending video by default as classified video can be viewed by unauthorized user

Yes please. Same here. We post confidential videos and everything is great except this one aspect of the product. I've assigned channels to departments associated channels with AD groups..etc. They want some assurance of security and I can't give it to them without being able to disable this feature.

Hi do we have any update on this feature?

This is needed. we post confidential videos on Stream with restricted audience, we do not even an the title on the Trending page.