[ci] Remove the broken Test examples workflow and its test suite (#98517)
Removes the `Test examples` workflow and its orphaned test suite. The
workflow fails every scheduled run: its pinned Playwright docker image
(v1.35.1) is incompatible with the Playwright version the repo now
requires (v1.61.0), so the browser cannot launch. It also no longer runs
what it was created for: since the `run-tests.js` glob root moved from
`test/` to the repository root, the `--type examples` string-prefix
filter `examples/` matches test files inside example apps instead of
`test/examples/examples.test.ts`, leaving that suite without any runner.
This deletes `.github/workflows/test_examples.yml`, the `test/examples/`
suite, and the `--type examples` filter in `run-tests.js`. The
`examples/` prefix stays in the default-run exclusion list so test files
inside example apps (which run with each example's own jest/vitest
setup) are still not picked up by bare `run-tests.js` invocations.
Co-authored-by: Claude Code <noreply@anthropic.com>