fix(playground): classify Gemini errors from their message, not metadata

[leoafarias]

Intent

Fix a real misclassification of Gemini errors in the Wizard. It was also the cause of the intermittent generation_model_client_test failures in CI (#129 and #132 each failed once on it today).

Root cause

• googleai_dart stamps every request with generateRequestId() = 'req_${DateTime.now().millisecondsSinceEpoch}'. ApiException.toString() appends that ID, the request URL, and the latency (403ms). This is unchanged in 13.0.0.
• ErrorClassifier checks 401/403/408/504/429 status codes structurally. For everything else, it substring-matched the whole toString() against patterns that include bare numbers: '429' for rate limits, and '401'/'403' for auth.
• Whenever the millisecond timestamp contained one of those numbers, the error was misclassified. Two examples:
  • A 400 "blocked by safety filters" was reported to the user as "API key is invalid".
  • A 503 "service unavailable" was reported as "The model is overloaded".

Fix (error_classifier.dart)

• googleai_dart errors (the sealed GoogleAIException) are matched on their message, not toString(), so the URL, request ID and latency never reach the patterns.
• Status-number patterns match only as whole numbers (\b429\b). A standalone "Error 429:" or "(403)" still matches; digits inside an ID, a timestamp or a duration don't. Word patterns keep substring matching, so their behavior is unchanged.

Tests

New deterministic regressions build an ApiException with request ID req_1790401403429 and a 403 ms latency. They check that a 400 safety block stays a safety block, a 503 "unavailable" stays unknown, and "API key not valid" is still recognized as authentication from the message. A plain-string case (14290 ms, job 1403) covers whole-number matching.

• All 4 regressions failed before the fix, each misclassified as a rate limit, and pass after it.
• The existing classifier tests pass unchanged.

Impacted packages

playground.

Commands run

• fvm dart analyze --fatal-infos in playground, including test_live: no issues.
• fvm flutter test in playground: 375 passing.
• generation_model_client_test.dart run 30 times in a row: 30/30 passing.

[github-actions]

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