✨ Add Hive integrations docs

[clubanderson]

Summary

• add /docs/hive/integrations with supported agent CLIs, inference engines, gateways, and infrastructure thanks
• add the page to Hive Overview navigation and generated sitemap inputs
• add metadata/JSON-LD and llms.txt crawler context

Validation

• npm ci
• npm run lint
• npm run test
• npm run check-links
• npm run build
• reverted prebuild rewrites with git checkout -- docs/content public/config/shared.json
• Playwright screenshots saved under ~/hive-work/docs-shots/site-int-docs-{dark,light}.png

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[clubanderson]

/lgtm
/approve

[kubestellar-prow]

@clubanderson: you cannot LGTM your own PR.

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[kubestellar-prow]

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This pull-request has been approved by: clubanderson

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[hivecommons-hive]

Read the diff against main and cross-checked the documented backend IDs against the hive codebase (v5 head). The Next.js changes are sound; one accuracy problem in the content should be fixed before this lands, because it is exactly the kind of thing operators will copy-paste.

Finding (medium): four backend: values in docs/content/hive/integrations.md are not valid hive backend IDs as written.

• Lines 128/135/142/149 document backend: openrouter, backend: anthropic, backend: openai, backend: deepseek.
• Hive's canonical lists are config.CLIBackends (claude, copilot, goose, codex, pi, bob, aider, gemini, agy, opencode, kilo, muse, omp — src/pkg/config/config.go:6014) and config.InferenceBackends (vllm, llm-d, litellm, watsonx — config.go:5974). All 17 of those entries in this page check out. ✅
• The other four are accepted only if the operator has configured a model gateway with that exact name (validateBackendName, src/pkg/agent/manager_routing.go:71 → routableBackend); otherwise the agent is rejected with unsupported backend "anthropic" (supported: …). There is also no built-in gateway kind anthropic/openai/deepseek — kinds are openrouter | litellm | vllm | llm-d | watsonx | custom (config.go:2539).
• Suggested fix: for OpenRouter, present it as a gateway (gateways: [{name: openrouter, kind: openrouter, …}] then backend: openrouter), and for Anthropic/OpenAI/DeepSeek drop the Hive config: backend: … line in favor of "reached via a configured gateway or the corresponding CLI backend".

Verified as correct:

• generateMetadata/JSON-LD wiring: the slug gate (hive/integrations) matches how getProjectFromSlug + getPageContent resolve the page (projectId === 'hive' && filePath === 'integrations.md'), and returning {} for all other slugs inherits parent metadata rather than clobbering it. JSON-LD is JSON.stringify of static constants — no injection surface.
• Nav entry in page-map.ts gives the page a static route; CI (TS/ESLint, unit tests, link check, Netlify preview) is green and the deploy preview renders the page.
• public/llms.txt matches the page's integration list.

— hive: agent=reviewer backend=copilot model=claude-fable-5 copilot=1.0.88