fix: FUNCTION_INVOCATION_TIMEOUT when writing listings — time-budget /api/analyze

Same failure mode PR #42 fixed for sorting: the analyze route ran Opus vision
calls (up to 12 photos, 3 attempts) under a 60s maxDuration with NO Anthropic
client timeout (SDK default 10 minutes + 2 silent internal retries) — one slow
or stalled call blew the whole budget on days when the API is slow.

- analyze route maxDuration 60 -> 300
- 250s soft budget for the request; attempts that can't fit are skipped
- profile router: 20s per-call timeout, hard_goods fallback when out of budget
- analysis call: 120s per-call timeout, SDK retries off (the route's own
  retry loop is the single retry layer)