[Docs] Diff /docs/api-reference against actual app/api/ routes

[ProfessorPolymorphic]

Context

app/docs/api-reference/page.tsx (177 LOC) lists REST endpoints for the platform. Sprint 2 added the friction-ledger work (work.ts reads, internal auth-gated views) and Sprint 3a added the similarity-preview endpoint (POST /api/similarity/preview); the API reference may have drifted.

Approach

Diff the documented endpoints against the actual filesystem:

find app/api -name "route.ts" | sort

For each endpoint that exists in the code:

• Verify documented method (GET/POST/PUT/DELETE) matches the exported handlers
• Verify documented request/response shapes match the actual code
• Add any new endpoints that aren't documented

For each endpoint documented but not in the code:

• Confirm it was retired and remove the doc entry

Known new endpoints to verify coverage

• POST /api/similarity/preview (Sprint 3a) — stateless similarity matching against partial assessment profile, threshold 0.2
• Any endpoints supporting /intake/[token] status reads
• Any endpoints under /api/registry or /api/submissions introduced for the ClickUp boundary

Acceptance criteria

• Every app/api/**/route.ts accounted for in the doc (documented or explicitly skipped)
• No documented endpoints that no longer exist
• Request/response shapes spot-checked against current handlers

[ProfessorPolymorphic]

Closed by #321.

All 12 routes under app/api/ and app/internal/ are now documented. The three that were missing entirely — POST /api/ask, POST /api/similarity/preview, and POST /internal/sync — are covered with their real contracts read off the route handlers: rate limits and headers, the deliberate 200-with-fallback on a MindRouter outage, the 0.2-vs-0.3 similarity threshold distinction, and 409-when-in-flight on sync.

Verified by diffing the documented paths against the route files rather than by inspection.