MCPServer handlers should raise exceptions, not return error objects

Comienza con _handle_call_tool() en src/mcp/server/mcpserver/server.py y _handle_request() en src/mcp/server/lowlevel/server.py, comparando sus rutas de excepciones y la construcción de respuestas. El trabajo está terminado cuando los handlers de alto nivel puedan señalar errores lanzando excepciones, los handlers de bajo nivel puedan devolver explícitamente ErrorData y las excepciones no controladas en cualquiera de las dos capas produzcan errores JSON-RPC bien formados sin filtrar detalles internos.

Problem

The current error handling across the two server layers is inconsistent and confusing for users. As noted by Marcelo, the experience should be more like Starlette's raise HTTPException pattern.

Current behavior

MCPServer (high-level) tool handlers:

• Raising any exception → caught by Tool.run(), re-wrapped as ToolError, then caught by _handle_call_tool() → CallToolResult(isError=True) (a JSON-RPC success response)
• Raising MCPError → re-raised past _handle_call_tool() → becomes a JSON-RPC error response
• Returning CallToolResult(isError=True) directly → also works
• Resource/prompt handlers have no try/except at the MCPServer layer — exceptions propagate to the low-level server

Low-level server handlers:

• _handle_request() catches MCPError → sends its .error as a JSON-RPC error
• Any other Exception → ErrorData(code=0, message=str(err)) → JSON-RPC error with non-standard code

Users need to understand the difference between ToolError, MCPError, CallToolResult(isError=True), and plain exceptions — each produces different behavior depending on which layer catches it.

Desired behavior

1. MCPServer users should raise exceptions to signal errors — the framework converts them to the appropriate protocol response. No need to construct and return error result objects.
2. Low-level server users should return ErrorData explicitly when they want to control the JSON-RPC error response, since they operate at the protocol level.
3. Unhandled exceptions at either layer should be caught gracefully by the framework and returned as a well-formed JSON-RPC error, without leaking internal details to the client.

Related issues

• #1742 — Introduce typed error classes with metadata (covers error taxonomy but not the raise-vs-return layering)
• #698 — Tool.run should not reveal exception value to the client (security concern with current behavior)
• #396 — Inconsistent Exception Handling in @app.call_tool (older, narrower scope)
• #1788 — Extensible pattern for protocol flow-control exceptions

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