Route SSE streaming through message broker

[IanLindsley]

Summary

• Replaces the direct engine proxy in the BFF streaming endpoint with the broker's two-step flow: POST to enqueue a message, then GET the SSE stream
• Adds a TransformStream that translates broker lifecycle events (queued, processing, done, error) into the existing client SSE format
• Zero browser-side changes — the BFF translates everything so use-chat-runtime.ts receives the same event format as before

Details

• src/app/api/chat/stream/route.ts — Rewritten to POST to BROKER_BASE_URL/api/v1/message (with X-API-Key auth), then GET BROKER_BASE_URL/api/v1/stream?user_id=X&message_id=Y, piping through a transform that maps broker events to the client's expected status/progress/complete/error format
• src/types/engine.ts — Added BrokerEnqueueRequest and BrokerEnqueueResponse types
• wrangler.jsonc — Added BROKER_BASE_URL to vars (BROKER_API_KEY must be set via wrangler secret put)
• History, preferences, and non-streaming chat still go directly to the engine (unchanged)

Test plan

• Send a message → verify SSE stream works through broker → verify AI response appears
• Verify broker lifecycle events (queued, processing, done) are translated correctly
• Send multiple rapid messages → verify they are processed in order
• Verify chat history and preferences still work (they bypass the broker)
• Test error scenarios: broker down, worker timeout
• Deploy: set BROKER_API_KEY as a Cloudflare secret

Closes #2

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