[PM-24345] Unable to install from App Store on iOS 15.x due to malformed Bundle Info.plist with WatchKit

### Steps To Reproduce

Have not been able to update Bitwarden iOS app for ages since mid last year. Finally have time to investigate what had happened. All Bitwarden versions after 2024.8.1 (including the latest version on App Store) suffer from a malformed Info.plist when bundling WatchKitApp. Updating to latest iOS is not an option due to company policy.

To reproduce, simply try and install Bitwarden from the App Store on any iOS device running iOS 15 (our devices are running iOS 15.4). Despite being compiled for iOS 8+, the app simply won't install or launch.

Affected versions are 2024.8.1+ with External Bundle Version Identifier 868104149+.

### Expected Result

App installs and launches.

### Actual Result

App does not install (fails at installd).

### Screenshots or Videos

Installd error log:

Found WatchKit 2.0 app at /var/installd/Library/Caches/com.apple.mobile.in-stalld.staging/temp/extracted/Payload/Bitwarden.app/Watch/BitwardenWatchApp.app but it does not have a WKWatchKitApp or WKApplication key set to true in its Info.plist

Last working version was 2024.7.1 with External Bundle Version Identifier 867769032.

### Additional Context

Installd error log:

Found WatchKit 2.0 app at /var/installd/Library/Caches/com.apple.mobile.in-stalld.staging/temp/extracted/Payload/Bitwarden.app/Watch/BitwardenWatchApp.app but it does not have a WKWatchKitApp or WKApplication key set to true in its Info.plist

### Build Version

2025.7.0

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

_No response_

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

Start by examining the WatchKit app's Info.plist and the iOS archive/build settings, using the reported installd error as the first diagnostic. Reproduce installation on an iOS 15.4 device or equivalent environment and compare the affected builds with the last working 2024.7.1 build. Done means the WatchKit bundle has the required key and the App Store build installs and launches on iOS 15.

Written by the indexing model from the issue text.