research: audit streaming/SSE support in loopover's API layer for chat-interface response streaming

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Context

Part of #6230 (chat interface spec, groundwork alongside the already-filed ui-primitives inventory issue #6244). A conversational chat surface needs to stream an agent's response incrementally rather than waiting for a full completion — this is standard for any chat UI. Before the chat interface's scope/backend decision lands, it's useful to know what streaming infrastructure this codebase already has to build on.

Requirements

• Audit src/api/routes.ts and any existing SSE/streaming implementation in this codebase — this session's earlier audit already found one real precedent: workers/mcp-session-hub.mjs-equivalent-style Durable Object SSE streaming exists in metagraphed's sibling repo for a comparable use case (resources/subscribe); check whether loopover has an equivalent pattern anywhere (a long-running Worker response, an existing SSE endpoint for any feature).
• Produce a short written inventory: what streaming infrastructure exists and is reusable, what would need to be built from scratch, and any Cloudflare Workers-specific constraints on long-lived streaming responses relevant to this repo's deployment model (self-hosted Worker + optional hosted).
• Do not build anything new — this is a research/audit deliverable only.

Deliverables

• A written inventory of existing streaming/SSE infrastructure and Workers-specific constraints, informing Spec: conversational chat interface for loopover (Lovable/Cursor-style) #6230's eventual implementation scoping.

Expected Outcome

Whoever eventually implements streaming chat responses (once #6230's scope is decided) starts from an accurate picture of what's reusable and what Workers-specific limits apply.

Links & Resources

• Spec: conversational chat interface for loopover (Lovable/Cursor-style) #6230 (parent spec), research: audit ui-kit for existing message/chat-adjacent UI primitives #6244 (the sibling UI-primitives inventory issue)
• src/api/routes.ts

[linear-code]

JSO-4401

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Moving to maintainer-only so contributors do not add raw .md files to the repo. We've migrated to a new Fumadocs setup which utilizes structured .mdx files in a proper hierarchy, now.

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Note: #6230's scope has now been decided (see its pinned comment) — the maintainer-facing chat panel (#6489) reuses `ai-chat-qa.ts` as-is, which returns a complete `ChatQaResult`, not a stream. So this audit is no longer a hard prerequisite for that implementation. Leaving this open since the inventory itself is still real, useful groundwork if a future streaming surface is ever scoped — just noting it's not blocking anything right now.