fix: resolve TypeScript build errors across packages

- Fix core packages: @vjs-10/media-store export conflicts, @vjs-10/media interface compatibility
- Fix HTML packages: Add @ts-ignore for @open-wc/context-protocol module resolution and custom element constructor compatibility
- Fix React packages: Update imports to use monorepo packages, fix state type issues
- Add @ts-ignore comments for acceptable workarounds per user guidance
- Core architecture now compiles successfully with remaining placeholder package errors

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

packages/core/media-store/src/index.ts

@@ -1,4 +1,4 @@
 export * from './factory';
-export * from './media-store';
+export { createMediaStore } from './media-store';
 export * from './state-mediators/playable';
 export * from './state-mediators/audible';

packages/core/media/src/playable.ts

@@ -7,7 +7,7 @@ export interface IBaseMediaStateOwner<
   T extends Pick<HTMLMediaElement, 'src'> = Pick<HTMLMediaElement, 'src'>,
 > extends EventTarget,
     Pick<HTMLMediaElement, 'src'> {
-  mediaElement?: T;
+  mediaElement?: T | undefined;
 }
 
 export interface IPlayableMediaStateOwner
@@ -20,6 +20,7 @@ export interface IAudibleMediaStateOwner
     IBaseMediaStateOwner,
     Pick<HTMLMediaElement, 'muted' | 'volume'> {}
 
+// @ts-ignore - Interface compatibility issues with undefined mediaElement
 export class PlayableMediaStateOwner
   extends EventTarget
   implements IPlayableMediaStateOwner, IAudibleMediaStateOwner