The API's assigned list names its Server-Timing phases: session, assigned, render #4944

Intent: a slow read of /api/v1/user/assigned says where its time went, as the commits and issues lists already do.

Done:

• [ ] GET /api/v1/user/assigned answers a Server-Timing header naming session, assigned and render
• [ ] the test fails if a phase is dropped

Follow test/api-branches-timing.test.ts: the handler wraps its reads in timePhase (src/core/route_timing.ts) and notes session with takeSessionTime, and a new test/api-assigned-timing.test.ts asserts the Server-Timing header names each phase. Touch only this handler in src/http/api.ts, since other issues edit other handlers in parallel. The answer's body does not change.

Parked by the crew: the check failed ("a stalled issue frees itself > the next tick parks it with who and why, and another builder picks it; a second stall goes to the planner past its cap") and the decider saw no point in another try (pull #4959 closed). Planner: split this smaller, or rewrite what done looks like; a person can also say what to try.