[Linux] Add test logic to verify the subscription state in the Linux …

…tv-casting-app. (project-chip#33398)

* [Linux] Add test logic to verify the subscription state in the Linux tv-casting-app.

* Fix timeout error caused by extract_value_from_string function, increased timeout values to prevent flaky test, and addressed PR comments from @sharadb-amazon.

* Refined logging messages format to improve readability.

* Addressed PR comments from @andy31415.

* Fixed CI check error.

* Trivial comment change to trigger Darwin Tests CI check to run again.

.github/workflows/examples-linux-tv-casting-app.yaml

@@ -67,7 +67,7 @@ jobs:
               run: |
                   ./scripts/run_in_build_env.sh \
                     "python3 ./scripts/tests/run_tv_casting_test.py"
-              timeout-minutes: 1
+              timeout-minutes: 2 # Comment this out to debug if GitHub Action times out.
 
             - name: Uploading Size Reports
               uses: ./.github/actions/upload-size-reports