Complete "Tools that are private to Apps" pattern documentation

Document the `_meta.ui.visibility: ["app"]` feature in `docs/patterns.md`
by referencing the existing type-checked example from
`src/server/index.examples.ts#registerAppTool_toolVisibility`.

- Fix typo: `["apps"]` → `["app"]` (singular)
- Remove placeholder function from `docs/patterns.ts`
- Expand description to explain use cases

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/server/index.examples.ts

@@ -86,11 +86,10 @@ function registerAppTool_basicUsage(server: McpServer) {
 }
 
 /**
- * Example: Tool visibility - create app-only tools for UI actions.
+ * Example: Model-only visibility - tools visible to model but not callable by UI.
  */
-function registerAppTool_toolVisibility(server: McpServer) {
-  //#region registerAppTool_toolVisibility
-  // Main tool - visible to both model and app (default)
+function registerAppTool_modelOnlyVisibility(server: McpServer) {
+  //#region registerAppTool_modelOnlyVisibility
   registerAppTool(
     server,
     "show-cart",
@@ -99,7 +98,7 @@ function registerAppTool_toolVisibility(server: McpServer) {
       _meta: {
         ui: {
           resourceUri: "ui://shop/cart.html",
-          visibility: ["model", "app"],
+          visibility: ["model"],
         },
       },
     },
@@ -108,8 +107,14 @@ function registerAppTool_toolVisibility(server: McpServer) {
       return { content: [{ type: "text", text: JSON.stringify(cart) }] };
     },
   );
+  //#endregion registerAppTool_modelOnlyVisibility
+}
 
-  // App-only tool - hidden from the model, only callable by the UI
+/**
+ * Example: App-only visibility - tools hidden from model, only callable by UI.
+ */
+function registerAppTool_appOnlyVisibility(server: McpServer) {
+  //#region registerAppTool_appOnlyVisibility
   registerAppTool(
     server,
     "update-quantity",
@@ -128,7 +133,7 @@ function registerAppTool_toolVisibility(server: McpServer) {
       return { content: [{ type: "text", text: JSON.stringify(cart) }] };
     },
   );
-  //#endregion registerAppTool_toolVisibility
+  //#endregion registerAppTool_appOnlyVisibility
 }
 
 /**

src/server/index.ts

@@ -117,8 +117,11 @@ export interface McpUiAppResourceConfig extends ResourceMetadata {
  * @example Basic usage
  * {@includeCode ./index.examples.ts#registerAppTool_basicUsage}
  *
- * @example Tool visibility - create app-only tools for UI actions
- * {@includeCode ./index.examples.ts#registerAppTool_toolVisibility}
+ * @example Tool visible to model but not callable by UI
+ * {@includeCode ./index.examples.ts#registerAppTool_modelOnlyVisibility}
+ *
+ * @example Tool hidden from model, only callable by UI
+ * {@includeCode ./index.examples.ts#registerAppTool_appOnlyVisibility}
  *
  * @see {@link registerAppResource} to register the HTML resource referenced by the tool
  */