What Chrome will and will not let an app hide
Two things about Chrome's screen-sharing behaviour that shaped how Perch works, both discovered by trying the other way first.
The sharing bar cannot be hidden#
When a tab is captured, Chrome shows its own sharing indicator. It is not part of the page, it is not part of any extension surface, and there is no flag, no policy and no CDP method that removes it.
That is correct behaviour. An indicator that an application could suppress would be worth exactly nothing — the entire point is that it is outside the control of whatever is doing the capturing.
So Perch does not try. The mirror is a separate window precisely so the thing you work in is not the thing wearing the banner.
A captured tab will not go window-fullscreen#
Ask a tab that is being captured to enter fullscreen and it will not. This is also deliberate: a page that could fill the screen the instant it started being captured is a phishing primitive.
The mirror handles fullscreen itself, on its own window, which is a different window from the captured one and therefore under no such restriction.
The general shape of both#
Every time I have found something Chrome will not let an application do around screen capture, the restriction has turned out to protect the person whose screen it is. Working with that has produced a better design than working around it would have: the mirror is a separate window because it has to be, and being a separate window is what lets you keep working while the other one is shared.