Improve exception tracebacks for easier debugging

[maxisbey]

Summary

Make exception tracebacks clearer and easier to understand by reducing asyncio/anyio wrapper noise.

Problem

• Exceptions are often wrapped in multiple layers of asyncio/anyio task group machinery
• Tracebacks are hard to read and don't clearly point to the root cause
• The raise_exception flag is not consistently respected
• Errors from deep inside task groups obscure the actual failure point

Goal

• Cleaner tracebacks that point to user code, not SDK internals
• Raise exceptions from the main context where possible
• Reduce nesting of exception wrappers

Related

• RuntimeError but the actual root cause is not logged correctly #743 - RuntimeError but the actual root cause is not logged correctly
• MCP Server: Inconsistent Exception Handling in @app.call_tool and Client Undetected Server Termination via Stdio #396 - MCP Server: Inconsistent Exception Handling in @app.call_tool
• ClientSession Error Handling #1401 - ClientSession Error Handling
• Introduce typed error classes with metadata #1742 - Introduce typed error classes with metadata

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_{AI Disclaimer}

[jagadeepmamidi]

Hi, I noticed this issue has been open for a while, so I wanted to check whether it is still relevant with the current codebase. If this is still something you'd like to improve, I'd be interested in working on it, particularly around reducing the asyncio/anyio exception wrapping and making the root errors easier to surface. If it's still open for contribution, could it be assigned to me?