Upgrade generative model to gemini-3-flash-preview

[NamanGoyalK]

Closes #3555

Updated the _geminiModel constant to models/gemini-3-flash-preview as requested.
This is a new pr identical to the now withdrawn #3558 which had a branch issue.

Verification

• Verified locally that dart-services starts correctly.
• Tested against the /api/v3/suggestFix endpoint and confirmed valid 200 OK responses.
• Confirmed models/gemini-3-flash-preview is the required endpoint for the current API release (Jan 2026).

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• I’ve reviewed the contributor guide and applied the relevant portions to this PR.

[github-actions]

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// Copyright (c) 2026, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

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pkgs/dart_services/lib/src/context.dart
pkgs/samples/lib/brick_breaker.dart
pkgs/samples/lib/fibonacci.dart
pkgs/samples/lib/hello_world.dart
pkgs/samples/lib/main.dart
pkgs/samples/lib/sunflower.dart

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[NamanGoyalK]

Hi @parlough, just a heads-up that I opened this clean PR to replace #3558 (to fix the git merge history).

Since you had requested a review from @johnpryan on the previous one, could you please re-assign him to this one? Thanks!