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

---

_{AI Disclaimer}