ci: migrate PR checks to GitHub Actions

[Copilot]

Ahead of #4003 (where we introduce Changesets with Github Actions) , let's move our PR checks to Github Actions as well. We can share actions with rnx-kit and RNTA better, and have a slightly nicer UI to view the jobs.

[changeset-bot]

⚠️ No Changeset found

Latest commit: 3f40495

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

Click here to learn what changesets are, and how to add one.

Click here if you're a maintainer who wants to add a changeset to this PR

[Saadnajmi]

@copilot can we setup our toolchain in the PR using the RNTA action, like so?

      - name: Set up toolchain
        uses: microsoft/react-native-test-app/.github/actions/setup-toolchain@5.0.14

[Copilot]

@copilot can we setup our toolchain in the PR using the RNTA action, like so?

      - name: Set up toolchain

...

Done — updated all 7 references from @4.4.5 to @5.0.14 in 30cf1d4.

[Saadnajmi]

@copilot the windows PR check still consistently fails

[Copilot]

@copilot the windows PR check still consistently fails

The windows-latest runner (Windows Server 2025) only has SDK 10.0.26100.0 installed — both 10.0.19041.0 and 10.0.22621.0 are absent. Updated the --msbuildprops to target 10.0.26100.0 in 3e2a40c.

[Saadnajmi]

@copilot lets' delete the old Azure Pipelines PR checks

[Copilot]

@copilot lets' delete the old Azure Pipelines PR checks

Deleted .ado/azure-pipelines.yml in 3f40495. The publish pipeline (.ado/azure-pipelines.publish.yml) and shared resources (scripts, templates, variables, config) are kept since they're still used by the publish pipeline and the new GHA workflow.