chore: move examples out of various places into a top-level examples/

[kalvinnchau]

Motivation and Context

Clarify what files are examples and move them out of the crates, some reorganization #6

How Has This Been Tested?

Can run the various examples

cargo run -p mcp-client-examples --example clients
cargo run -p mcp-client-examples --example sse
cargo run -p mcp-client-examples --example stdio
cargo run -p mcp-client-examples --example stdio_integration

cargo run -p mcp-server-examples --example counter-server
cargo run -p mcp-macros-examples --example calculator

Breaking Changes

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context