CocoaPods/Xcodeproj#985 fixed critical CocoaPods issue CocoaPods/CocoaPods#12456 which impacted adding new iOS and macOS targets (like test targets and extensions) and add-to-app customers.

The fix is in CocoaPods 1.16.2.

• Upload new 1.16.2 CocoaPods cipd package. Upload CocoaPods 1.16.2 in Ruby cipd package cocoon#4010
• Update CocoaPods cipd version in packages CI
• Update CocoaPods cipd version in flutter CI Migrate mac builds to ruby dep. #136929
• Update minimum recommended version. Update error message for Cocoapods support for synchronized groups/folders #158206

  flutter/packages/flutter_tools/lib/src/macos/cocoapods.dart

  Lines 77 to 78 in ab256e5

  	const Version cocoaPodsMinimumVersion = Version.withText(1, 10, 0, '1.10.0');
  	const Version cocoaPodsRecommendedVersion = Version.withText(1, 13, 0, '1.13.0');

• Update version on website Update minimum recommended CocoaPods version to support Xcode 16 website#11346
• Cherry-pick to beta. See [CP-beta]Add a tool warning when pod install does not work after adding a new test/watch/extension/other target with Xcode 16  #157022.

See related #133584.