#19307: docs: add Google (Gemini) provider documentation

## Summary - Problem: No documentation page exists for Google/Gemini providers despite all three auth methods being fully implemented in code. - Why it matters: Users have no docs to reference when setting up Gemini API key, Gemini CLI OAuth, or Google Antigravity OAuth. - What changed: Added `docs/providers/google.md` with setup instructions for all three Google auth methods, added the page to Mintlify navigation and provider index, and updated plugin `docsPath` references. - What did NOT change (scope boundary): No code logic changes; only docs and `docsPath` string updates in the two Google plugin extensions. ## Change Type (select all) - [x] Docs ## Scope (select all touched areas) - [x] Integrations - [x] UI / DX ## Linked Issue/PR - N/A ## User-visible / Behavior Changes - New doc page at `/providers/google` covering Gemini API key, Gemini CLI OAuth, and Antigravity OAuth setup. - Google entry added to the provider index page and Mintlify sidebar navigation. - Plugin "docs" links now point to `/providers/google` instead of the generic `/providers/models`. ## Security Impact (required) - New permissions/capabilities? `No` - Secrets/tokens handling changed? `No` - New/changed network calls? `No` - Command/tool execution surface changed? `No` - Data access scope changed? `No` ## Repro + Verification ### Environment - OS: Linux - Runtime/container: Node 22, Mintlify dev server ### Steps 1. Run `mintlify dev` in `docs/` 2. Navigate to `/providers/google` 3. Verify all three auth options render correctly 4. Check sidebar navigation includes Google under Providers 5. Check provider index page links to the new page ### Expected - Page renders with frontmatter, three auth options (API key, Gemini CLI OAuth, Antigravity OAuth), notes, and troubleshooting sections. ### Actual - Page renders as expected. ## Evidence - [x] Verified locally via Mintlify dev server ## Human Verification (required) - Verified scenarios: Page renders correctly in Mintlify dev, navigation links work, all CLI commands and model IDs match implementation. - Edge cases checked: All provider IDs, env vars, and default models verified against source code. - What you did **not** verify: Production Mintlify deployment. ## Compatibility / Migration - Backward compatible? `Yes` - Config/env changes? `No` - Migration needed? `No` ## Failure Recovery (if this breaks) - How to disable/revert this change quickly: Revert commit. - Files/config to restore: `docs/docs.json`, `docs/providers/index.md`, plugin `index.ts` files. - Known bad symptoms reviewers should watch for: Broken Mintlify nav or 404 on the new page. ## Risks and Mitigations None <!-- greptile_comment --> <h3>Greptile Summary</h3> Added comprehensive documentation for Google/Gemini provider authentication covering all three supported methods (API key, Gemini CLI OAuth, and Antigravity OAuth). Updated Mintlify navigation config and provider index page to include the new doc. Plugin `docsPath` fields now correctly point to `/providers/google` instead of the generic `/providers/models`. All provider IDs, model IDs, environment variables, and CLI commands match the implementation code. <h3>Confidence Score: 5/5</h3> - This PR is safe to merge with no risk - Documentation-only change with no code logic modifications. All technical details verified against source code (provider IDs, model names, env vars, CLI commands). Follows existing documentation patterns and Mintlify conventions from AGENTS.md. Navigation and plugin references properly updated. - No files require special attention _{Last reviewed commit: 4b13499} <!-- greptile_other_comments_section --> _{(2/5) Greptile learns from your feedback when you react with thumbs up/down!} <!-- /greptile_comment -->