refactor: remove StdioServerParameters class

[QuantGeekDev]

client/stdio and client/sse use two different patterns for initialization, this PR tries to standardize it after discussions with @Kludex by removing StdioServerParameters

Motivation and Context

Continuation to the discussion here: #300

How Has This Been Tested?

Testing with Claude Desktop's config

Breaking Changes

This is a breaking change to how Stdio is initialized, it is no longer done via StdioServerParameters

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

[Kludex]

I don't think we want to add breaking changes, so we'd support both, and add a deprecation warning when using settings parameter.

[QuantGeekDev]

I don't think we want to add breaking changes, so we'd support both, and add a deprecation warning when using settings parameter.

Got it, that makes sense. I'll add implementation and test cases for this

[QuantGeekDev]

@Kludex Do you think it makes sense to add this, or are we going to see an overhaul here with the changes from the new spec? I can get this in over the weekend

[mcp-shadow]

Thank you for your contribution to standardizing the MCP Python SDK initialization patterns. Your effort to improve code consistency is appreciated, but we need to ensure backward compatibility during the transition.

[Kludex]

Can this bot not close PRs?