[material_ui] Port flutter/flutter #190206 "Prevent stale async suggestions in SearchAnchor"

[cuishuang]

Ports flutter/flutter#190206 to material_ui following flutter/flutter#188444.

Fixes flutter/flutter#190205.

This change prevents an older asynchronous SearchAnchor.suggestionsBuilder request from replacing the results of a newer request.

It assigns an incrementing ID to each suggestions request and only applies the result when it still represents the latest request.

Pre-Review Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the AI contribution guidelines and understand my responsibilities, or I am not using AI tools.
• I read the Tree Hygiene page, which explains my responsibilities.
• I read and followed the relevant style guides and ran the auto-formatter.
• 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 linked to at least one issue that this PR fixes in the description above.
• I followed the version and CHANGELOG instructions, using semantic versioning and the repository CHANGELOG style, or I have commented below to indicate which documented exception this PR falls under¹.
• I updated/added any relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or I have commented below to indicate which test exemption this PR falls under¹.
• All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel on Discord.

Note: The Flutter team is currently trialing the use of Gemini Code Assist for GitHub. Comments from the gemini-code-assist bot should not be taken as authoritative feedback from the Flutter team. If you find its comments useful you can update your code accordingly, but if you are unsure or disagree with the feedback, please feel free to wait for a Flutter team member's review for guidance on which automated comments should be addressed.

Footnotes

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. ↩ ↩²

[gemini-code-assist]

Code Review

This pull request updates SearchAnchor to prevent stale asynchronous suggestions from overwriting newer results. It introduces an internal counter, _suggestionsCallId, to track suggestion requests and discard results from outdated calls. A new test case has been added to verify that out-of-order asynchronous suggestions are ignored. No review comments were provided, and there is no feedback to provide.