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>

docs/patterns.md

@@ -6,11 +6,11 @@ title: Patterns
 
 This document covers common patterns and recipes for building MCP Apps.
 
-## [TODO] Tools that are private to Apps
+## Tools that are private to Apps
 
-Use `Tool._meta.ui.visibility: ["apps"]` to make tools only visible to Apps.
+Set {@link types!McpUiToolMeta.visibility Tool.\_meta.ui.visibility} to `["app"]` to make tools only callable by Apps (hidden from the model). This is useful for UI-driven actions like updating quantities, toggling settings, or other interactions that shouldn't appear in the model's tool list.
 
-{@includeCode ./patterns.ts#privateTools}
+{@includeCode ../src/server/index.examples.ts#registerAppTool_appOnlyVisibility}
 
 ## [TODO] Authenticated calls from App
 

docs/patterns.ts

@@ -9,17 +9,6 @@
 
 import { App } from "../src/app.js";
 
-// TODO: Add imports as patterns are implemented
-
-/**
- * Example: Tools that are private to Apps
- */
-function privateTools() {
-  //#region privateTools
-  // TODO: Tool._meta.ui.visibility: ["apps"]
-  //#endregion privateTools
-}
-
 /**
  * Example: Authenticated calls from App
  */
@@ -121,7 +110,6 @@ function migrateFromOpenai() {
 }
 
 // Suppress unused variable warnings
-void privateTools;
 void authenticatedCalls;
 void errorsToModel;
 void hostStyling;