[ci] Roll repo tooling and add readme-check

[stuartmorgan-g]

• Rolls the pinned repo tooling to pick up the updated readme-check.
• Enables readme-check in CI, which I apparently forgot to ever do for this repository.
• Enables the secondary run with --require-excerpts, plus an opt-out list for all the current violations, so we can migrate incrementally.
• Fixes the few missing language tags so that the primary readme-check passes.
• Adds the submodule with the excerpt tools, and the task that runs excerpting, to allow for adopting excerpting in the future without repo-level changes.
  • As in flutter/plugins, cloning the submodule is not required for most use cases, so this should not cause disruption.

Brings flutter/packages in line with the recent flutter/plugins changes.

No version change: Adding language tags in READMEs is too minor to warrant releasing
No CHANGELOG change: Adding language tags in READMEs is too minor to warrant a mention

Part of flutter/flutter#102679

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 relevant style guides and ran the auto-formatter. (Unlike the flutter/flutter repo, the flutter/packages repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the package surrounded by square brackets, e.g. [shared_preferences]
• I listed at least one issue that this PR fixes in the description above.
• I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or this PR is exempt from version changes.
• I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style.
• 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.
• All existing and new tests are passing.

[flutter-dashboard]

It looks like this pull request may not have tests. Please make sure to add tests before merging. If you need an exemption to this rule, contact Hixie on the #hackers channel in Chat (don't just cc him here, he won't see it! He's on Discord!).

If you are not sure if you need tests, consider this rule of thumb: the purpose of a test is to make sure someone doesn't accidentally revert the fix. Ask yourself, is there anything in your PR that you feel it is important we not accidentally revert back to how it was before your fix?

Reviewers: Read the Tree Hygiene page and make sure this patch meets those guidelines before LGTMing.

[Hixie]

test-exempt: is a test.

[ditman]

LGTM! Let's get the snippets auto-extracted!