Partially resolves[^1] https://github.com/flutter/flutter/issues/139774.

Effectively reverts https://github.com/flutter/flutter/pull/125581.

The main change here is that I deleted and recreated the macos Xcode project for this integration test (hence the large diff). I tried fixing the existing project first, but it was set up quite differently, and—for whatever reason—the integration test would get stuck trying to load `dev/integration_tests/flavors/integration_test/integration_test.dart`.

I verified that this works locally, but I don't know if it's possible to run this on the devicelab try pool to verify that it works on devicelab hardware.

[^1]: I would not close the issue until 1) this PR lands, 2) the integration test consistently passes on CI, and 3) macOS support for flavors is publicly documented.