Click required to update theme after system theme switch

### Windows Terminal version

1.22.11141.0

### Windows build number

10.0.26100.3915

### Other Software

_No response_

### Steps to reproduce

I use AutoDark to automatically switch the system theme between Light/Dark at particular hours.

When a theme switch happens, most applications also switch the theme.

But Windows Terminal doesn't. It keeps the old theme, and only updates it after activating the Terminal window. So after any automatic system switch, I need to manually click all Windows Terminal windows to make them respect the theme too, which is annoying.

### Expected Behavior

Windows Terminal automatically switches it's theme when the system theme changes.

### Actual Behavior

Click is required for Windows Terminal to update it's theme

Reproduce the issue on Windows Terminal 1.22.11141.0 while changing the system theme with AutoDark, then trace how theme changes are handled when the window is inactive versus activated. Done means every open Terminal window updates automatically when the system theme switches, without requiring a click; add or update coverage if the relevant test entry point is found.

Written by the indexing model from the issue text.