[business_analysis] Unify Projects edit UI code to single

_Automatically composed from the parent epic at dispatch time._

PRD settled. Projects edit hangs because console writes are bare fetch with no relay (api.ts:68). Operator chose: relay writes once with an idempotency key; fold all network paths (reads/writes, stragglers, streams, terminal, browser URLs) into one gate-enforced choke point; unify edit pages on useEditRecord + useSubmit. The architect must first confirm the hang in Nick's telemetry (AC-0). Memory: none applied.