FCE-2869: Add permission helpers docs (#234)

## Description

- **managing-devices.mdx**: Add "Managing Permissions (Mobile only)"
section documenting `useCameraPermissions` and
`useMicrophonePermissions` hooks with query/request API and usage
example
- **installation.mdx**: Replace
`expo-permissions`/`react-native-permissions` recommendation with a link
to the new Managing Permissions section
- Bump `web-client-sdk` submodule

## Motivation and Context

The mobile SDK now ships built-in permission hooks
(`useCameraPermissions`, `useMicrophonePermissions`), so the docs should
guide users to those instead of third-party libraries.

Author: MiloszFilimowski

docs/how-to/client/installation.mdx

@@ -221,12 +221,10 @@ export default function App() {
 ## Camera and Microphone Permissions
 
 :::info
-You don't need to explicitly request permissions as they're automatically asked for when your app needs them.
+You don't need to explicitly request permissions — they're automatically requested when your app calls `initializeDevices()`.
 :::
 
-The SDK automatically requests camera and microphone permissions when you call `initializeDevices()`. The system permission dialog will be shown to the user if permissions haven't been granted yet.
-
-If you need manual control over permissions, you can use the [expo-permissions](https://docs.expo.dev/versions/latest/sdk/permissions/) or [react-native-permissions](https://github.com/zoontek/react-native-permissions) libraries.
+If you need manual control over when permissions are requested, see [Managing Permissions](./managing-devices#managing-permissions-mobile-only).
 
   </TabItem>
 </Tabs>

docs/how-to/client/managing-devices.mdx

@@ -252,3 +252,58 @@ export function MicrophoneControl() {
   );
 }
 ```
+
+## Managing Permissions (Mobile only)
+
+The SDK provides built-in hooks for querying and requesting device permissions: `useCameraPermissions` and `useMicrophonePermissions` from `@fishjam-cloud/react-native-client`.
+
+Both hooks return a `[query, request]` tuple:
+
+- **`query()`** — checks the current permission status without prompting the user
+- **`request()`** — triggers the native permission dialog and returns the resulting status
+
+The returned `PermissionStatus` is one of: `'granted'`, `'denied'`, or `'prompt'`.
+
+:::info
+Requesting permissions manually is optional — `initializeDevices()` will automatically prompt for any permissions that haven't been granted yet.
+However, you must always call `initializeDevices()` to set up camera and microphone devices.
+:::
+
+#### Usage Example
+
+```tsx
+// @noErrors: 2305
+import React, { useEffect } from "react";
+import {
+  useCameraPermissions,
+  useMicrophonePermissions,
+  useInitializeDevices,
+} from "@fishjam-cloud/react-native-client";
+
+function RoomScreen() {
+  const [queryCamera, requestCamera] = useCameraPermissions(); // [!code highlight]
+  const [queryMicrophone, requestMicrophone] = useMicrophonePermissions(); // [!code highlight]
+  const { initializeDevices } = useInitializeDevices(); // [!code highlight]
+
+  useEffect(() => {
+    const setup = async () => {
+      let cam = await queryCamera();
+      let mic = await queryMicrophone();
+
+      if (cam !== "granted") cam = await requestCamera();
+      if (mic !== "granted") mic = await requestMicrophone();
+
+      if (cam === "granted" && mic === "granted") {
+        await initializeDevices(); // [!code highlight]
+      }
+    };
+    setup();
+  }, [
+    queryCamera,
+    requestCamera,
+    queryMicrophone,
+    requestMicrophone,
+    initializeDevices,
+  ]);
+}
+```