The unfocused background flashes briefly when switching between tabs

### Windows Terminal version (or Windows build number)

1.8+

### Other Software

_No response_

### Steps to reproduce

slap

```json
"unfocusedAppearance": {
"background": "#888888"
}

```

in a profile

### Expected Behavior

Maybe there's a way we can not switch to the unfocused appearance when the control is removed from the UI tree entirely? IIRC we were talking about doing a similar thing to prevent the DxRender from doing _anything_ when the tab is inactive

### Actual Behavior

Switching between tabs with the same profile briefly flashes the gray color as it fades to the active color. It doesn't look great :confu

Reproduce the flash by configuring a profile with unfocusedAppearance.background set to #888888, then switching between tabs using that profile. Start by tracing tab removal from the UI tree and the related DxRender activity. Done means the unfocused color no longer briefly appears during the transition, while the expected appearance behavior remains intact.

Written by the indexing model from the issue text.