feat: Support Gemini 3 built-in and custom tool combinations (tool context circulation)

[roomote-v0]

Related GitHub Issue

Closes: #11966

Description

This PR attempts to address Issue #11966 by enabling "tool context circulation" for Gemini 3+ models. Feedback and guidance are welcome.

Key changes:

1. src/api/providers/gemini.ts: Added isGemini3Model() helper to detect Gemini 3+ models. For these models, Google Search is included as a built-in tool alongside custom function declarations in the tools config. The streaming handler now processes executableCode and codeExecutionResult parts from server-side tool invocations, surfacing them as text to the user and storing them for history round-tripping via a new getServerSideToolParts() method.

2. src/api/transform/gemini-format.ts: Added ServerSideToolContentBlock type and isServerSideToolContentBlock() guard. The converter now recognizes executableCode and codeExecutionResult content blocks in conversation history and converts them back to proper Gemini Part format for round-tripping.

3. src/core/task/Task.ts: Updated addToApiConversationHistory() to retrieve server-side tool parts from the handler and persist them as content blocks in the conversation history, enabling context circulation across turns.

Design decisions:

• Gated entirely behind isGemini3Model() check -- older Gemini models and other providers are completely unaffected.
• Server-side tool outputs are surfaced as formatted text (code blocks) to the user rather than a new stream event type, keeping the change minimal.
• The ServerSideToolPart type uses a generic data: Record<string, unknown> payload to preserve all API fields verbatim for future-proofing.

Test Procedure

• Added tests in gemini.spec.ts verifying: googleSearch is included for Gemini 3 models; not included for pre-Gemini 3 models; executableCode/codeExecutionResult parts are handled in streaming and stored; parts are reset between requests.
• Added tests in gemini-format.spec.ts verifying: executableCode and codeExecutionResult content blocks are round-tripped correctly; mixed function calls and server-side tool parts work together.
• Updated existing gemini-handler.spec.ts test to reflect the new combined tools behavior for the default Gemini 3 model.
• All 60 tests across 4 test files pass. TypeScript compilation and linting pass cleanly.

Run: cd src && npx vitest run api/providers/__tests__/gemini.spec.ts api/providers/__tests__/gemini-handler.spec.ts api/transform/__tests__/gemini-format.spec.ts

Pre-Submission Checklist

• Issue Linked: This PR is linked to an approved GitHub Issue (see "Related GitHub Issue" above).
• Scope: My changes are focused on the linked issue (one major feature/fix per PR).
• Self-Review: I have performed a thorough self-review of my code.
• Testing: New and/or updated tests have been added to cover my changes.
• Documentation Impact: No documentation updates are required for this internal API change.
• Contribution Guidelines: I have read and agree to the Contributor Guidelines.

Documentation Updates

• No documentation updates are required.

Additional Notes

• The @google/genai SDK v1.29.1 does not expose an explicit includeServerSideToolInvocations flag in its TypeScript types. Instead, Gemini 3 natively supports combining googleSearch and functionDeclarations in the same tools array without additional flags.
• The -customtools model variant (gemini-3.1-pro-preview-customtools) is unrelated to this feature per the issue discussion -- it is for prioritizing custom tool use over basic shell commands.

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