Add announce support to the engine

[ash2moon]

Partly of #165510

⤵️ Child PR: #168992

Partly re-lands #165531
The PR was originally reverted due to an issue with an internal Google test. I split re-land PR into two separate ones so that we can individually revert in case it fails again.

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the Flutter Style Guide, including Features we expect every widget to implement.
• I signed the CLA.
• I listed at least one issue that this PR fixes in the description above.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or this PR is test-exempt.
• I followed the breaking change policy and added Data Driven Fixes where supported.
• All existing and new tests are passing.

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[chunhtai]

LGTM, left a suggestion on web platform

[auto-submit]

autosubmit label was removed for flutter/flutter/169685, because - The status or check suite Linux web_tool_tests has failed. Please fix the issues identified (or deflake) before re-applying this label.

[auto-submit]

autosubmit label was removed for flutter/flutter/169685, because - The status or check suite ci.yaml validation has failed. Please fix the issues identified (or deflake) before re-applying this label.