refactor: converge chat dispatch on the canonical Agents API REST contract

## Problem

Frontend Agent Chat implements `/frontend-agent-chat/v1/chat` and independently rebuilds input normalization, permission handling, `agents/chat` execution, and response projection while Agents API already owns `/agents-api/v1/chat`.

Relevant implementation: `inc/rest.php:17-63,417-486`.

## Impact

Attachment handling, client context, authorization, errors, and response semantics can drift across two public adapters.

## Acceptance criteria

- Keep product bootstrap/session behavior in Frontend Agent Chat.
- Consume the canonical Agents API chat transport contract for dispatch and normalization.
- Retain only a documented product response projection where necessary.
- Add parity tests for permissions, attachments, context, errors, and streaming/non-streaming responses.

Found while reviewing Extra Chill's production composition of Frontend Agent Chat and Agents API.

Start by reading inc/rest.php:17-63 and 417-486, then compare the frontend chat route with the canonical /agents-api/v1/chat contract. Trace normalization, permissions, attachments, context, errors, and streaming/non-streaming responses. Done means product bootstrap/session behavior remains, dispatch uses the canonical transport, any product projection is documented, and parity tests cover the listed cases.

Written by the indexing model from the issue text.