feat(inference): add OpenWork inference proxy

[src-opn]

Summary

• Add an OpenWork-managed inference proxy app backed by OpenRouter, including proxy routes, webhook settlement, key validation, usage buckets, and model aliasing.
• Add Den API ownership for inference enablement, per-member inference keys, org upstream OpenRouter keys, OpenWork LLM provider rows, and post-member-change sync hooks.
• Add Den Web inference controls and update Den Web/Desktop provider parsing so source: openwork providers are visible/importable.

Evidence

Build verification

• pnpm --filter @openwork-ee/den-db build -- passed
• pnpm --filter @openwork/types build -- passed
• pnpm --filter @openwork-ee/inference build -- passed
• pnpm --filter @openwork-ee/den-api build -- passed
• pnpm --filter @openwork-ee/den-web build -- passed
• pnpm --filter @openwork/app build -- passed

API verification

• Local inference proxy received POST /api/v1/chat/completions and returned 200 during desktop app testing.
• Manual curl confirmed auth reaches the proxy; model alias handling was updated so both model1 and openwork/model1 are accepted.

UI verification

• Den Web build passes for the new Inference page and OpenWork provider source support.
• Full Chrome MCP screenshot/video evidence not captured yet.
• Known follow-up: desktop active-session UI can remain on Thinking until switching sessions, despite the proxy returning 200; this draft PR captures the current implementation state for review.

Test instructions

1. Set OPENROUTER_MANAGEMENT_API_KEY in ee/apps/den-api/.env.local.
2. Run pnpm run dev:web-local.
3. Open Den Web and enable OpenWork Models from the Inference tab.
4. Confirm /api/den/v1/llm-providers returns an openwork provider with models openwork/model1 and openwork/model2.
5. In the desktop app, import/use the OpenWork Models provider and send a message.
6. Confirm the inference service logs POST /api/v1/chat/completions and returns 200.

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Project	Deployment	Actions	Updated (UTC)
openwork-app	Ready	Preview, Comment	May 13, 2026 1:44am
openwork-den	Ready	Preview, Comment	May 13, 2026 1:44am
openwork-den-worker-proxy	Ready	Preview, Comment	May 13, 2026 1:44am
openwork-landing	Ready	Preview, Comment, Open in v0	May 13, 2026 1:44am
openwork-share	Ready	Preview, Comment	May 13, 2026 1:44am