Replace Zod with Standard Schema for validation

**Is your feature request related to a problem? Please describe.**
This SDK currently uses Zod directly for schema validation. However, the Standard Schema specification has been developed as a common interface for JavaScript/TypeScript schema libraries. The creators of Zod (along with Valibot and ArkType) designed this specification to make it easier for ecosystem tools to accept user-defined type validators without needing custom adapters for each library.

**Describe the solution you'd like**
Please consider replacing direct Zod usage with Standard Schema. This would allow users to:

Choose their preferred validation library (Zod, Valibot, ArkType, etc.)
Benefit from the "integrate once, validate anywhere" philosophy of Standard Schema
Follow best practices recommended by schema library authors

The change should be fairly straightforward since:

Zod already implements the Standard Schema interface (in v3.24.0+)
The Standard Schema interface is designed to be minimal and easy to integrate

**Would you be willing to contribute this feature?**

- [ ] Yes, I would like to contribute this feature
- [x] No, I'm just suggesting the idea

I took [this feature request in fastmcp](https://github.com/punkpeye/fastmcp/issues/26) for inspiration when creating this.

Start by locating the SDK's direct Zod validation usage and the entry points that accept schemas. Read the Standard Schema specification alongside the existing validation flow, then confirm that supported Standard Schema-compatible validators work without Zod-specific coupling and that the existing validation behavior remains covered by the repository's tests.

Written by the indexing model from the issue text.