Relands #149568, which was reverted in https://github.com/flutter/flutter/pull/149998 due to unverified golden tests post-commit from recent infra issues.
**New changes** (all contained in 5ca5139d43 ):
* Fixes a problem within the tests "Overall looks correctly under x theme" where the button press is not applied to the golden file.
* Dark theme now uses colors different from the light theme. It was an issue reported in https://github.com/flutter/flutter/pull/149568#issuecomment-2161392381. I made the mistake because the XCode preview doesn't correctly apply dark theme, which made me think the dark theme uses the same colors. As shown in the following table, the dark theme colors also achieved deviation of <=1.
<img width="1091" alt="image" src="https://github.com/flutter/flutter/assets/1596656/f4acda2b-1857-449c-8c1b-1f48afeb9095">
Screenshot comparison: (left to right: native, Flutter after PR, Flutter before PR)
<img width="1286" alt="image" src="https://github.com/flutter/flutter/assets/1596656/580eef1f-a7f9-45d9-a7c8-fab0ca9606e3">