It seems that dart pub publish --dry-run is failing in main because dependencies for example directories are not being fetched, which is causing new analyze errors that weren't being surfaced before. See: dart-lang/pub#3618.

This PR modifies the publish-check command to recurse into every example of each package being analyzed, and getting its dependencies before the actual pub publish command runs.

Works around: dart-lang/pub#3618

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/plugins repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the plugin 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.

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