refactor(examples): inline SDK calls in every story; isolate machinery; add shape-check

[felixweinberger]

Inline serveStdio/createMcpHandler/toNodeHandler/Client/transport construction explicitly in every example story; isolate runner machinery from the example code.

Motivation and Context

Examples are compiled documentation — when the SDK API changes, 25 compile errors flag 25 doc pages. Hiding the transport setup behind runServerFromArgs/connectFromArgs defeats that. Users browsing examples/ should see exactly what they'd write.

How Has This Been Tested?

run:examples 65/65 legs, typecheck, lint (incl. new no-restricted-imports public-only rule), docs:check.

Breaking Changes

None.

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 or updated documentation as needed

Additional context

• parseExampleArgs/check/runClient/siblingPath → @mcp-examples/shared (workspace package, clearly scaffolding).
• Runner → scripts/examples/run-examples.ts.
• examples/eslint.config.mjs: bans @modelcontextprotocol/core, */src/*, */dist/*, and the deleted harness — examples can only reach the published surface.
• Stories that don't fit the canonical stdio-or-http shape (Hono adapter, sessionful-2025 demos, interactive REPL, gateway prior-connect, auth scaffolding, etc.) explain why in their file-header doc comment.
• examples/harness.ts deleted; examples/CONTRIBUTING.md gains a "Canonical shape" section.

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