## Background
The Windows runner has a race at startup:
1. **Platform thread**: creates a hidden window
2. **Platform thread**: launches the Flutter engine
3. **UI/Raster threads**: renders the first frame
4. **Platform thread**: Registers a callback to show the window once the next frame has been rendered.
Steps 3 and 4 happen in parallel and it is possible for step 3 to complete before step 4 starts. In this scenario, the next frame callback is never called and the window is never shown.
As a result the `windows_startup_test`'s test, which [verifies that the "show window" callback is called](1f09a8662d/dev/integration_tests/windows_startup_test/windows/runner/flutter_window.cpp (L60-L64)), can flake if the first frame is rendered before the show window callback has been registered.
## Solution
This change makes the runner schedule a frame after it registers the next frame callback. If step 3 hasn't completed yet, this no-ops as a frame is already scheduled. If step 3 has already completed, a new frame will be rendered, which will call the next frame callback and show the window.
Part of https://github.com/flutter/flutter/issues/119415
See this thread for alternatives that were considered: https://github.com/flutter/engine/pull/42061#issuecomment-1550080722
Check in linux and windows platform code now that they are stable, so that we could use in devicelab in the future. Removed the ICO from the windows example to avoid analysis check, and since it won't be important for benchmarking or UI tests
