feat(cc-config): add and remove MCP servers through the claude CLI

Mutation goes through `claude mcp add|remove`, never a direct edit of
~/.claude.json — the running CLI rewrites that file concurrently, so a
dashboard write would race it. Reads stay on readMcpServers.

The plan specified a --url flag; the real CLI (v2.1.266) has none —
commandOrUrl is positional, and --header must trail it or the variadic
flag swallows the url. Built against the verified shape.

openapi.yaml

@@ -2094,6 +2094,21 @@ components:
           description: MCP servers scoped to the current project root in ~/.claude.json.
           items:
             $ref: '#/components/schemas/CcConfigMcpServer'
+    CcConfigCliResult:
+      type: object
+      required:
+        - ok
+        - stdout
+        - stderr
+      properties:
+        ok:
+          type: boolean
+          enum:
+            - true
+        stdout:
+          type: string
+        stderr:
+          type: string
     CcConfigHookEntry:
       type: object
       description: A single flattened hook command bound to a matcher.
@@ -7996,6 +8011,108 @@ paths:
                     url: https://mcp.example.com/sse
                     headers:
                       - Authorization
+  /api/cc-config/mcp/add:
+    post:
+      tags:
+        - CcConfig
+      summary: Add an MCP server
+      description: 'Mutating. Runs `claude mcp add` — never a direct edit of ~/.claude.json, which the running CLI rewrites concurrently. Body carries either `url` (+ optional `transport: http|sse` and `headers`) for a remote server, or `command` + `args` (+ optional `env`) for a stdio server; exactly one of the two forms is required. `scope` is required and is `user`|`project` only — not the settings union''s third `project-local` value, which is a different axis. A non-zero CLI exit is returned as 422, not 500. Emits a `cc_config_changed` websocket event on success.'
+      operationId: ccConfigPostMcpAdd
+      requestBody:
+        required: true
+        content:
+          application/json:
+            schema:
+              type: object
+              required:
+                - name
+                - scope
+              properties:
+                name:
+                  type: string
+                  example: vercel
+                scope:
+                  type: string
+                  enum:
+                    - user
+                    - project
+                  example: user
+                transport:
+                  type: string
+                  enum:
+                    - http
+                    - sse
+                url:
+                  type: string
+                  example: https://mcp.vercel.com
+                headers:
+                  type: object
+                  additionalProperties:
+                    type: string
+                  example:
+                    Authorization: Bearer xyz
+                command:
+                  type: string
+                  example: npx
+                args:
+                  type: array
+                  items:
+                    type: string
+                  example:
+                    - '-y'
+                    - server-github
+                env:
+                  type: object
+                  additionalProperties:
+                    type: string
+                  example:
+                    GITHUB_TOKEN: xxx
+      responses:
+        '200':
+          description: The CLI's stdout/stderr on success.
+          content:
+            application/json:
+              schema:
+                $ref: '#/components/schemas/CcConfigCliResult'
+        '400':
+          description: Bad name/scope/args, or an incompatible combination.
+        '422':
+          description: The CLI exited non-zero (e.g. the name is already taken).
+  /api/cc-config/mcp/remove:
+    post:
+      tags:
+        - CcConfig
+      summary: Remove an MCP server
+      description: Mutating. Runs `claude mcp remove`. `scope` (`user`|`project`) narrows which config layer to remove from; omit it to let the CLI find the server wherever it exists. A non-zero CLI exit (e.g. the name does not exist) is returned as 422. Emits a `cc_config_changed` websocket event on success.
+      operationId: ccConfigPostMcpRemove
+      requestBody:
+        required: true
+        content:
+          application/json:
+            schema:
+              type: object
+              required:
+                - name
+              properties:
+                name:
+                  type: string
+                  example: vercel
+                scope:
+                  type: string
+                  enum:
+                    - user
+                    - project
+      responses:
+        '200':
+          description: The CLI's stdout/stderr on success.
+          content:
+            application/json:
+              schema:
+                $ref: '#/components/schemas/CcConfigCliResult'
+        '400':
+          description: Bad name/scope.
+        '422':
+          description: The CLI exited non-zero (e.g. no such server).
   /api/cc-config/hooks:
     get:
       tags: