How many Apple TV 4K's can I have in our House?

My family and I have 6 separate 4K HDR compatible TV's throughout the house, and we all love our Apple TV 4K HDR experiences. But how many Apple TV 4K's can I have in one house before it's a problem?

Currently we only have (2) Apple TV 4K's, and (1) Apple TV 3rd Gen.

To date, we've always logged in to these devices using my primary Apple account because the TV's could theoretically be used by anyone in the house.

Is this unlimited, where I can just buy as many Apple TV 4K's as I have TV's - or do I need to worry about not being able to be on 2 TV's in separate rooms at the same time when streaming?

Or does that only apply to when 'streaming from the library' (I'm almost never 'streaming from my iTunes library'). Or does that limitation apply to just when streaming Apple TV+ content as well? Or does it apply to when using the devices for any streaming services in general (Netflix, Amazon Prime, YouTube, Hulu, etc.)?

Or is this logging in somehow limited by how many other Apple devices I have... because I happen to have quite a lot of those as well...

We'd love to get all these screens standardized onto a single device-type (instead of having Fire-sticks here, Fire-cubes there, Roku here, SmartTV OS there... and so on