Migrate `ext-apps` to `@modelcontextprotocol/server` v2 SDK

[khandrew1]

I'm starting work on a new major version of our MCP SDK based on the new beta package for @modelcontextprotocol/server. The ext-apps repo still depends on the older v1 of the package causing some issues with developing.

Considering that the v2 SDK will be releasing soon, I'd like to start work on migrating this repo to the new version SDK as well so we can all be prepared.

[khandrew1]

There's no easy upgrade path for App/AppBridge, which subclass Protocol I saw this PR that says "Protocol stays private (dispatcher RFC handles framework subclassing)." and the Gist for the Dispatcher RFC. Though everything I see related to it is closed and can't find an update on its status.