Dozer [0] doesn't require any special permissions. I guess this is needed by Bartender because it creates a little pop-out menu that shows the icons somewhere else?

[0] https://github.com/aonez/Dozer/releases/tag/v4.2.1-silicon

If true, that's a wild permissions model

You wouldn't want your mouse driver, for example, being able to see _every_ piece of software in your menu bar by default without extra permissions?

The case for "I need to see what apps are in the menu bar" is so rare there's no setting for it -> "screen recording" is the closest one.

Among many. Apple’s security model has a lot of ups and downs like this. I gather any app that needs access to anything on the screen outside of itself requires “screen recording” permission. I know all of the Remote Desktop apps, as well as color sampling functions in browsers, Adobe’s apps, and all of the designer tools with similar functionality require it.

It isn't a permissions model, it's explicitly a hack.