compose: Offer video capture on iOS

Thanks to the recent upgrade of react-native-image-picker, which had
a small change to support 'mixed' in `launchCamera`:
  react-native-image-picker/react-native-image-picker@4de5e5a39
If we end up having to revert that upgrade because of something
unrelated, that change should be easy to patch in with
`patch-package`; see b546b07 for an example of using
patch-package.

Fixes: zulip#5733

ios/ZulipMobile/Info.plist

@@ -54,6 +54,8 @@
 	<string>By allowing camera access, you can take photos and send them in Zulip messages.</string>
 	<key>NSLocationWhenInUseUsageDescription</key>
 	<string></string>
+	<key>NSMicrophoneUsageDescription</key>
+	<string>By allowing microphone access, you can take videos and send them in Zulip messages.</string>
 	<key>NSPhotoLibraryAddUsageDescription</key>
 	<string>Save photos you choose from Zulip to your photo library.</string>
 	<key>NSPhotoLibraryUsageDescription</key>

src/compose/ComposeMenu.js

@@ -259,7 +259,25 @@ export default function ComposeMenu(props: Props): Node {
 
     launchCamera(
       {
-        mediaType: 'photo',
+        // Here's how iOS video recording works in an attempt on iOS 16:
+        //   - iOS gives a native interface with a camera preview. You can
+        //     choose "photo" or "video", with "photo" selected by default.
+        //   - On tapping "video" for the first time, it shows a permissions
+        //     prompt with the NSMicrophoneUsageDescription string. (If we
+        //     didn't declare that string, the app would hang here.)
+        //   - If you grant the permission, the interaction proceeds as
+        //     you'd hope: you take a video (or cancel), then confirm,
+        //     retake, or cancel.
+        //   - If you don't grant the permission, it proceeds similarly,
+        //     except the sent video will have no sound. Later interactions
+        //     will also let you take video without sound, and you won't get
+        //     prompted about permissions (!). If you want to record videos
+        //     with sound, you have to look in Settings by yourself and
+        //     grant the permission there.
+        //
+        // 'mixed' is not supported on Android:
+        //   https://github.com/react-native-image-picker/react-native-image-picker#options
+        mediaType: Platform.OS === 'ios' ? 'mixed' : 'photo',
 
         // On Android ≤9 (see above) and on iOS, this means putting up a
         // scary permission request. Shrug, because other apps seem to save