docs: update embedme references and fix line numbers

[M-jerez]

Summary

This PR updates all embedme references in the documentation to reflect the current state of the codebase after the run-types refactor.

Changes Made

Fixed embedme references:

• Updated file paths and line numbers that were outdated due to code refactoring
• Fixed line number references in:
  • packages/router/src/types/definitions.ts (RouteDef, HookDef, HeaderHookDef, RawHookDef)
  • packages/router/src/types/handlers.ts (Handler interface)
  • packages/router/src/types/context.ts (MionRequest, MionResponse, MionHeaders)
  • packages/core/src/types.ts (RpcErrorParams, PublicRpcError)
  • packages/router/src/types/publicMethods.ts (PublicMethod)
  • packages/client/src/types.ts (SubRequest, RouteSubRequest, HookSubRequest)
  • packages/router/src/types/general.ts (RouterOptions)

Updated documentation content:

• Changed .validate() to .typeErrors() in client examples to match current API
• Created missing packages/router/examples/extending-routes-and-hooks.routes.ts file
• Ran embedme to update all code blocks with current source code

Files updated:

• website/content/1.introduction/2.quick-start.md
• website/content/2.docs/1.routes.md
• website/content/2.docs/2.hooks.md
• website/content/2.docs/3.call-context.md
• website/content/2.docs/4.client.md
• website/content/2.docs/5.request-and-response.md
• website/content/2.docs/6.error-handling.md
• All platform-specific documentation files

Testing

• ✅ All embedme references now point to correct files and line numbers
• ✅ npm run lint passes with no errors
• ✅ npm run format applied successfully
• ✅ npx embedme website/content/**/*.md runs successfully and updates code blocks

Notes

• Excluded package-lock.json from commit as instructed
• All documentation now accurately reflects the current codebase structure
• The embedme tool can now be run successfully to keep documentation in sync

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Pull Request opened by Augment Code with guidance from the PR author