Verify and access react-native-worklets before module installation

[michalsek]

Closes #RNAA-366

Introduced changes

• adds react-native-worklets verification as a api installation step
• adds missing semver dependency (used by build-time script)
• adds AudioAPIModule class as a singleton layer to interact with the native module

Checklist

• Linked relevant issue
• Updated relevant documentation
• Added/Conducted relevant tests
• Performed self-review of the code
• Updated Web Audio API coverage
• Added support for web

[Copilot]

Pull request overview

This PR introduces a singleton AudioAPIModule class to centralize react-native-worklets verification and native module installation, improving the initialization flow and preventing potential crashes when worklets/reanimated are not properly imported.

Key changes:

• Introduces AudioAPIModule singleton to handle worklets verification before native module installation
• Refactors worklets access throughout the codebase to use the new centralized module
• Adds semver as a production dependency (previously only used by build scripts)

Reviewed changes

Copilot reviewed 45 out of 48 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
packages/react-native-audio-api/src/AudioAPIModule/AudioAPIModule.ts	New singleton class that verifies worklets availability and version, manages audio runtime creation, and handles native module installation
packages/react-native-audio-api/src/AudioAPIModule/index.ts	Barrel export for AudioAPIModule
packages/react-native-audio-api/src/AudioAPIModule/globals.d.ts	Global type declarations moved from api.ts for better organization
packages/react-native-audio-api/src/utils/index.ts	Refactored to use AudioAPIModule singleton instead of local worklets state
packages/react-native-audio-api/src/api.ts	Simplified to import AudioAPIModule and export public API (removed inline installation logic)
packages/react-native-audio-api/src/core/AudioContext.ts	Uses AudioAPIModule.getOrCreateAudioRuntime() instead of direct worklets module access
packages/react-native-audio-api/src/core/OfflineAudioContext.ts	Uses AudioAPIModule.getOrCreateAudioRuntime() instead of direct worklets module access
packages/react-native-audio-api/src/core/BaseAudioContext.ts	Uses AudioAPIModule.workletsModule for creating shareable worklets
packages/react-native-audio-api/src/system/AudioManager.ts	Removed native module installation logic (now handled by AudioAPIModule)
packages/react-native-audio-api/package.json	Added semver ^7.7.3 as a production dependency
yarn.lock	Lockfile update for semver dependency
packages/react-native-audio-api/scripts/validate-worklets-version.js	Minor formatting improvements
apps/common-app/src/App.tsx	Removed Animated.addWhitelistedNativeProps call and import reordering
apps/fabric-example/ios/Podfile.lock	Updated RNScreens dependency version
packages/react-native-audio-api/common/cpp/**/*.h	C++ code formatting: standardized opening brace placement for function definitions

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[maciejmakowski2003]

great job!!! could you update your clang-format version and fix formatting issues?

[poneciak57]

LGTM