[Sycun]

Allow administrators to omit the optional store field for a Chat Completions channel whose gateway rejects it. Pi can otherwise send store: false to unknown endpoints; the settings connection probe does not send this field.

This is an explicit per-channel opt-in using the existing request extensions:

reasoning:
  extra_request_fields:
    store: null

For Chat Completions only, this setting disables Pi's automatic storage field and removes the null extension before sending. Unconfigured channels retain Pi's existing behavior; explicit store: false and store: true remain intact. No endpoint/domain heuristics are added. Claude and Responses adapters retain their existing behavior. Existing local-profile compatibility remains unchanged.

Validation:

• Real Go → Pi worker → HTTP tests cover default, explicit false, explicit true, and explicit omission, with streaming usage and tool declarations retained.
• Configuration tests cover official/default/custom endpoints, non-mutation of the channel configuration, and isolation from Claude/Responses adapters.
• go test ./internal/multiagent ./internal/reasoning ./internal/config ./internal/agentruntime passed.
• Pi TypeScript build and all 17 runtime tests passed in the initial validation; runtime source/dependencies are unchanged by this PR.

Tests use local gateway fixtures. The originally reported third-party service was not tested directly, so this PR does not claim to establish the rejected field for that incident.