[T1][URGENT] Migrate coder-client Chats API to /api/v2 (chat lifecycle + events + org-scoped models) #187

Parent

Epic: #186

What to build

Migrate the coder-client crate's Coder Chats API integration off the experimental paths and onto the GA /api/v2 surface introduced in Coder v2.37.0. This is the urgent, code-correctness half of the migration.

• Chat lifecycle (REST): create_chat, get_chat, get_chat_opt, list_chats, send_chat_message, get_chat_messages, archive_chat, interrupt_chat → change the base path from /api/experimental/chats to /api/v2/chats (crates/coder-client/src/lib.rs).
• Chat events (WebSocket): ChatStream::connect → change the stream path from /api/experimental/chats/{id}/events to /api/v2/chats/{id}/events (crates/coder-client/src/chat_stream.rs).
• Model resolution (URGENT — already broken): list_chat_models currently calls GET /api/experimental/chats/models, which was removed immediately in v2.37 (PR #28632). Re-point it to GET /api/v2/organizations/{organization}/chats/models, resolving the organization via the client's existing get_default_organization_id and keeping the response-shape parsing consistent.

Acceptance criteria

• All chat lifecycle calls hit /api/v2/chats (no /api/experimental/chats left in coder-client runtime code).
• ChatStream connects to /api/v2/chats/{id}/events.
• list_chat_models calls the org-scoped v2 models endpoint using a resolved org id, and still returns the model list used for the model hint.
• cargo check --workspace --all-features passes.

Blocked by

None (can start immediately). Highest priority — the models endpoint already fails against :latest (= v2.37.0).

Evidence

• Chats API promoted experimental → /api/v2 (PR #28496, one-month window, removed in v2.38): feat: mount chat API routes under /api/v2 coder/coder#28496
• GA release notes / BREAKING CHANGES: https://github.com/coder/coder/releases/tag/v2.37.0
• Chat-model routes removed immediately (PR #28632): https://github.com/coder/coder/releases/tag/v2.37.0
• Repo source-of-truth record: docs/architecture/coder-v2.37-migration.md §1.3