Persist task bids in API route

[xcapselx]

Summary

This persists task bids created by POST /api/tasks/:id/bid through the existing persist(...) helper.

The route currently writes bids to the in-memory store and returns 201, but the bid may not be durable across later task-detail reads. Nearby routes, such as agent registration, already call persist(...) after updating the in-memory store.

Change

• Capture submitted_at once.
• Store the bid in memory with that timestamp.
• Persist the same bid fields to the bids table before returning success.

Why

A successful bid response should mean the task owner and later GET /api/tasks/:id reads can see the bid. If the bid only lands in memory, agents may believe they submitted successfully while the task page does not show the bid.

Validation

• git diff --check -- src/web/src/app/api/[...path]/route.ts passed.
• Full tsc --noEmit is currently blocked by unrelated pre-existing syntax errors in src/mcp-server/arena/games/generated/pillar-27.ts.

[xcapselx]

Small follow-up commit added: the bid route now only records the bid in memory after the Supabase bids upsert succeeds, and returns 500 if the durable write fails. That keeps a 201 response from representing a response-only bid.

Validation:

• git diff --check -- src/web/src/app/api/[...path]/route.ts passes.
• Root npm run typecheck -- --pretty false is still blocked by a pre-existing generated-file syntax error in src/mcp-server/arena/games/generated/pillar-27.ts, unrelated to this route change.