Introduce a unified Virtual Threads friendly API

The MCP Java SDK team and myself would like to acknowledge the strong desire to evolve the MCP Java SDK to leverage Virtual Threads as a key building block.

This issue is about introducing a new unified Virtual Threads friendly API with the following characteristics:

• Natively designed for Virtual Threads both in terms of idiomatic API and implementation
• Designed with Structured Concurrency in mind but SC will not be required
• Introduce a new way to expose streaming based features
• Extensible design that should allow changing the implementation
• No dependency on Reactor or Reactive Streams
• No Sync or Async prefix
• Technically could run on Java 21+ but Java 25+ (latest LTS version without the thread pinning issue) will be the recommended baseline

The Sync and Async API and implementation would remain close to what they are today for now, to not break existing use cases and remain fully compatible with Java 17+, while the new unified API would potentially mean a changed module hierarchy where Project Reactor is not a required dependency.

A prototype of this unified Virtual Threads friendly API, using the Sync API as the starting point but achieving the characteristics shared above, will be shared in this issue or via a related PR and discussed with the community to gather feedback and hopefully reach a consensus.

Start by reviewing the existing Sync and Async APIs and the current module hierarchy, then compare their Reactor and Reactive Streams dependencies with the proposed Java 21+/25+ direction. The issue provides no files or tests to run; progress means producing and discussing a prototype that meets the listed Virtual Threads, streaming, extensibility, and dependency requirements and reaches community consensus.