docs: add Claude Desktop as a supported client (#30653)

Closes
[DOCS-1198](https://linear.app/codercom/issue/DOCS-1198/document-claude-desktop-as-a-supported-coder-client)

Adds Claude Desktop alongside the other supported clients and IDEs. Once
the Coder CLI is installed and logged in, running workspaces appear in
Claude Desktop.

## Changes

- New page `docs/user-guides/workspace-access/claude-desktop.md`:
prerequisites, setup, troubleshooting.
- New `## Claude Desktop` section in `workspace-access/index.md`.
- Registered the page in `docs/manifest.json`.
- Added Claude Desktop to the IDE list in the glossary.

## Notes

- Setup steps checked against `docs/reference/cli/` and the existing SSH
docs.
- `make fmt/markdown`, `lint/markdown`, `lint/docs-manifest`,
`lint/emdash`, `lint/docs-html` pass.

> 🤖 This PR was created with the help of Coder Agents, and needs a human
review. 🧑💻

docs/manifest.json

@@ -375,6 +375,11 @@
 							"title": "Antigravity",
 							"description": "Access your Coder workspace with the Antigravity agentic code editor over SSH.",
 							"path": "./user-guides/workspace-access/antigravity.md"
+						},
+						{
+							"title": "Claude Desktop",
+							"description": "Let Claude Desktop access your Coder workspaces.",
+							"path": "./user-guides/workspace-access/claude-desktop.md"
 						}
 					]
 				},

docs/manifest/user-guides/workspace-access.yml

@@ -40,3 +40,6 @@ children:
   - title: Antigravity
     description: Access your Coder workspace with the Antigravity agentic code editor over SSH.
     path: ./user-guides/workspace-access/antigravity.md
+  - title: Claude Desktop
+    description: Let Claude Desktop access your Coder workspaces.
+    path: ./user-guides/workspace-access/claude-desktop.md

docs/reference/glossary.md

@@ -540,7 +540,7 @@ Refer to [Support bundle](../support/support-bundle.md).
 
 ### Supported editors and IDEs
 
-The editors and IDEs that connect to Coder workspaces, including [VS Code](../user-guides/workspace-access/vscode.md), [code-server](../user-guides/workspace-access/code-server.md), [Cursor](../user-guides/workspace-access/cursor.md), [Devin Desktop](../user-guides/workspace-access/devin-desktop.md), [Antigravity](../user-guides/workspace-access/antigravity.md), [Zed](../user-guides/workspace-access/zed.md), and JetBrains IDEs through [Gateway](../user-guides/workspace-access/jetbrains/gateway.md) and [Toolbox](../user-guides/workspace-access/jetbrains/toolbox.md).
+The editors and IDEs that connect to Coder workspaces, including [VS Code](../user-guides/workspace-access/vscode.md), [code-server](../user-guides/workspace-access/code-server.md), [Cursor](../user-guides/workspace-access/cursor.md), [Devin Desktop](../user-guides/workspace-access/devin-desktop.md), [Antigravity](../user-guides/workspace-access/antigravity.md), [Claude Desktop](../user-guides/workspace-access/claude-desktop.md), [Zed](../user-guides/workspace-access/zed.md), and JetBrains IDEs through [Gateway](../user-guides/workspace-access/jetbrains/gateway.md) and [Toolbox](../user-guides/workspace-access/jetbrains/toolbox.md).
 
 ### Swagger
 

docs/user-guides/workspace-access/claude-desktop.md

@@ -0,0 +1,58 @@
+---
+title: Claude Desktop
+---
+
+[Claude Desktop](https://claude.com/download) is Anthropic's desktop app for Claude.
+Claude Desktop can list your running Coder workspaces, so you can connect to them from the app.
+
+> [!NOTE]
+> This integration is implemented by Claude Desktop, not by Coder.
+> Anthropic's documentation doesn't currently describe it, and the behavior can change between Claude Desktop versions.
+
+## Prerequisites
+
+- [Claude Desktop](https://claude.com/download) installed on your local machine.
+- The [Coder CLI](../../install/cli.md) installed and on your `PATH`.
+- The Coder CLI authenticated with your deployment:
+
+  ```sh
+  coder login <deployment-url>
+  ```
+
+- At least one running workspace.
+
+## Set up Claude Desktop
+
+1. Install the Coder CLI and confirm `coder version` works in your terminal.
+
+1. Authenticate the CLI with your deployment:
+
+   ```sh
+   coder login <deployment-url>
+   ```
+
+1. Restart Claude Desktop.
+   Your running workspaces appear in Claude Desktop.
+
+## Troubleshooting
+
+If your workspaces don't appear in Claude Desktop, check the following:
+
+1. The Coder CLI is installed and on your `PATH`.
+   Run `coder version`.
+1. You're logged in.
+   Run `coder login <deployment-url>` if needed.
+1. The workspace is running.
+
+## Next steps
+
+Claude Desktop connects to workspaces you already have.
+To explore other ways to use Claude with Coder:
+
+- [Agent Relay for Claude Code](../../ai-coder/agent-relay/claude-code.md):
+  run Claude Code's cloud sessions inside self-hosted Coder workspaces.
+  Unlike the Claude Desktop integration, Agent Relay orchestrates the workspaces itself.
+  It creates a workspace from a template for each session and deletes it when the session ends, instead of using your existing workspaces.
+  Visit the [Agent Relay overview](../../ai-coder/agent-relay/index.md) for how it works.
+- [Claude Code with AI Gateway](../../ai-coder/ai-gateway/clients/claude-code.md):
+  route Claude Code running in a workspace through AI Gateway.

docs/user-guides/workspace-access/index.md

@@ -165,6 +165,13 @@ Antigravity connects using the Coder extension.
 
 Read more about [using Antigravity with your workspace](./antigravity.md).
 
+## Claude Desktop
+
+[Claude Desktop](https://claude.com/download) is Anthropic's desktop app for Claude.
+Once the Coder CLI is installed and logged in, your running workspaces appear in Claude Desktop.
+
+Read more about [using Claude Desktop with your workspace](./claude-desktop.md).
+
 ## JetBrains IDEs
 
 We support JetBrains IDEs using