docs: Update API documentation for CLI installation IPC handlers

- Document new CLI installation IPC handlers (isStudioCliInstalled, installStudioCli, uninstallStudioCli)
- Add detailed installedAppsApi endpoint documentation
- Update RTK Query API section with CLI installation hooks
- Update last modified date to 2025-11-10

Co-authored-by: Fredrik Rombach Ekelund <undefined@users.noreply.github.com>

Author: github-actions[bot]

docs/ai-instructions.md

@@ -146,6 +146,11 @@ window.ipcApi.openSiteURL(id)     // Send (one-way)
 // Main (src/ipc-handlers.ts) handles:
 ipcMain.handle('startServer', async (event, siteId) => { ... })
 ipcMain.on('openSiteURL', (event, id) => { ... })
+
+// CLI Installation API (delegated to src/modules/cli/lib/installation):
+window.ipcApi.isStudioCliInstalled() // Check CLI installation status
+window.ipcApi.installStudioCli()     // Install the CLI
+window.ipcApi.uninstallStudioCli()   // Uninstall the CLI
 ```
 
 ### 3. WordPress Provider Pattern (Strategy Pattern)
@@ -169,8 +174,17 @@ Both implement the `WordPressProvider` interface with methods:
 - provider constants: WordPress/PHP versions
 - RTK Query APIs for data fetching:
   - wpcomApi: WordPress.com API calls
-  - installedAppsApi: System apps detection
+  - installedAppsApi: System apps detection, CLI installation status
   - wordpressVersionsApi: Available WP versions
+
+// installedAppsApi endpoints (src/stores/installed-apps-api.ts):
+- getStudioCliIsInstalled: Query CLI installation status
+- getInstalledApps: Query installed editors and terminals
+- getUserEditor: Get user's preferred editor
+- getUserTerminal: Get user's preferred terminal
+- saveStudioCliIsInstalled: Mutation to install/uninstall CLI
+- saveUserEditor: Mutation to save preferred editor
+- saveUserTerminal: Mutation to save preferred terminal
 ```
 
 ### 5. Site Management
@@ -353,6 +367,6 @@ Local component state used for temporary UI interactions.
 
 ---
 
-Last Updated: 2025-11-05
+Last Updated: 2025-11-10
 Repository: https://github.com/Automattic/studio
 License: GPLv2 or later