[google_sign_in] Add contributor setup instructions

[stuartmorgan-g]

Adds a CONTRIBUTING.md that explains how to configure the example app for manual testing, since we don't currently maintain a central project for testing it.

Also opportunistically fixes a minor latent mistake in an older CHANGELOG entry, so that the next publication will include that fix.

Fixes https://github.com/flutter/flutter/issues/83759 Fixes https://github.com/flutter/flutter/issues/167906

Pre-Review Checklist

• [x] I read the Contributor Guide and followed the process outlined there for submitting PRs.
• [x] I read the Tree Hygiene page, which explains my responsibilities.
• [x] I read and followed the relevant style guides and ran the auto-formatter.
• [x] I signed the CLA.
• [x] The title of the PR starts with the name of the package surrounded by square brackets, e.g. [shared_preferences]
• [x] I linked to at least one issue that this PR fixes in the description above.
• [x] I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or I have commented below to indicate which version change exemption this PR falls under[^1].
• [x] I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style, or I have commented below to indicate which CHANGELOG exemption this PR falls under[^1].
• [x] I updated/added any relevant documentation (doc comments with ///).
• [x] I added new tests to check the change I am making, or I have commented below to indicate which test exemption this PR falls under[^1].
• [x] All existing and new tests are passing.

[^1]: Regular contributors who have demonstrated familiarity with the repository guidelines only need to comment if the PR is not auto-exempted by repo tooling.