feat: add Coder Agents chat tools to the MCP toolsdk (#28025)

Exposes the experimental Coder Agents chats API through the MCP tool
registry, so MCP clients (the hosted `/api/experimental/mcp/http` server
and `coder exp mcp server`) can start and drive server-side coding
agents.

New tools in `codersdk/toolsdk`, all thin wrappers over existing
`codersdk.ExperimentalClient` methods:

| Tool | Wraps |
|---|---|
| `coder_create_chat` | `CreateChat` (prompt, optional org, model
config, labels) |
| `coder_get_chat` | `GetChat` (status, last error, last turn summary,
workspace, files) |
| `coder_get_chat_messages` | `GetChatMessages` (user-facing parts,
chronological, cursor pagination, queued prompts) |
| `coder_send_chat_message` | `CreateChatMessage` (queue or interrupt
busy behavior) |
| `coder_interrupt_chat` | `InterruptChat` |
| `coder_archive_chat` | `UpdateChat` with `archived: true` |
| `coder_list_chat_model_configs` | `ListChatModelConfigs` (enabled
configs with default flag) |

Both MCP servers register tools from `toolsdk.All`, so no additional
wiring is needed. Responses are trimmed to what an MCP caller needs (IDs
as strings, user-facing transcripts) rather than full SDK payloads. No
new endpoints and no database changes.

Also adds MCP
[prompts](https://modelcontextprotocol.io/specification/2026-07-28/server/prompts)
for the chat workflows, defined once in `codersdk/toolsdk` and
registered by both servers:

| Prompt | Purpose |
|---|---|
| `coder_agents_delegate` | delegate a task to a Coder Agents chat and
monitor it to completion |
| `coder_agents_check` | check the status and recent activity of an
existing chat |

Each prompt declares the tools its workflow needs; the stdio server
skips prompts whose tools are excluded by `--allowed-tools`.

Tests run the tools against a chat-enabled coderdtest instance (fake
OpenAI-compatible provider plus in-process AI bridge), covering the full
lifecycle, an interrupt against a blocked turn, pagination cursors,
permission-dependent model config filtering, and argument validation.
Prompt coverage spans SDK rendering, the hosted
`prompts/list`/`prompts/get` round trip, and the stdio server including
allowlist gating.

> Mux created this PR on Mike's behalf.

docs/ai-coder/mcp-server.md

@@ -199,6 +199,7 @@ The MCP server exposes tools across several areas:
 - **File operations**: read, write, and edit files in a workspace
 - **Workspace interaction**: run commands, forward ports, list apps, and read logs
 - **Task management**: create, list, inspect, and control tasks
+- **Coder Agents chats**: create chats, send messages, read transcripts and status, interrupt, archive, and list available models
 - **User and system**: authenticated user details, tar uploads, and task reporting
 
 The full, authoritative set of tools, including their names, descriptions, and
@@ -206,6 +207,18 @@ arguments, is defined in Coder's
 [`toolsdk` package](../../codersdk/toolsdk/toolsdk.go). Refer to it for the
 current list, since the available tools can change between releases.
 
+## Available Prompts
+
+The MCP server also exposes
+[prompts](https://modelcontextprotocol.io/specification/2026-07-28/server/prompts)
+for common Coder Agents chat workflows. Clients that support prompts surface
+them for you to invoke, for example as slash commands:
+
+- `coder_agents_delegate`: delegate a coding task to a Coder Agents chat and
+  monitor it to completion
+- `coder_agents_check`: check the status and recent activity of an existing
+  Coder Agents chat
+
 ## Troubleshooting
 
 ### "Unauthorized" errors