CI: Check for pub publish --dry-run errors for the Flutter package

[Nidal-Bakir]

New Issue Checklist

• I am not disclosing a vulnerability.
• I am not just asking a question.
• I have searched through existing issues.
• I can reproduce the issue with the latest version of Parse Server and the Parse Flutter SDK.

Issue Description

The current CI does not account for dart pub publish errors

Steps to reproduce

See https://github.com/parse-community/Parse-SDK-Flutter/actions/runs/4304405195/jobs/7505394193
Our last publish fails due to an error from dart pub publish. so we need a way to check for these errors in the ci.yml file so we can spot them immediately.

Actual Outcome

Error when trying to publish to pub.dev

Expected Outcome

The error should be spotted before the publishing stage.

[parse-github-assistant]

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[parse-github-assistant]

The label type:feature cannot be used in combination with type:ci.

[parse-github-assistant]

The label type:ci cannot be used in combination with type:feature.