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.

server/openapi-extra/cc-config.js

@@ -387,6 +387,18 @@ const schemas = {
     },
   },
 
+  /** Response of a successful mutating `claude mcp …` run. A non-zero CLI
+   *  exit arrives as an HTTP 422 error instead of one of these. */
+  CcConfigCliResult: {
+    type: "object",
+    required: ["ok", "stdout", "stderr"],
+    properties: {
+      ok: { type: "boolean", enum: [true] },
+      stdout: { type: "string" },
+      stderr: { type: "string" },
+    },
+  },
+
   // ── Hooks ────────────────────────────────────────────────────────────
   CcConfigHookEntry: {
     type: "object",
@@ -1580,6 +1592,98 @@ const paths = {
     },
   },
 
+  "/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: ["CcConfig"],