/llms.txt lists every MCP tool from the generated tool index, and a test fails when one is missing #5939

Replaces #5903. Both of its pulls failed at the preview deploy (#5919, #5920), and both edited src/http/mcp.ts, the file 61 open pulls collide on. It waits for #5924's split, so the list comes from the generated index, not from that file.

Done when:

• [ ] /llms.txt has a ## MCP tools section with one line per tool: name: description, plus (admin) or (writes) where it applies. It is read from the generated tool index at boot, and it does not filter by the reader.
• [ ] A test compares the section with the index and fails on any difference.
• [ ] Before pushing, start the app (bun run src/server.ts) and request / and /llms.txt. Both must answer 200, which is what the preview deploy checks. Put both status lines in the pull.
• [ ] /llms.txt keeps its cache headers.