feat: Adjust log levels for trace logging

[kyle-leonhard]

Reduce log levels on per-connection/request/message events to trace from info.

I considered using DEBUG which is the default level used by Axum for request logging. WDYT?

Motivation and Context

Emitting per-connection and message logs at INFO level is unexpected, in my experience. Using a finer level allows filtering to be effective without requiring users to set module level configuration.

How Has This Been Tested?

Locally with my MCP server

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 appropriate error handling
• I have added or updated documentation as needed

Additional context

None