fix: propagate McpError from tool handlers as JSON-RPC error

[mengyunxie]

Motivation and Context

When a tool handler raises McpError, both the lowlevel server's call_tool decorator and FastMCP's Tool.run() catch it via except Exception and wrap it as CallToolResult(isError=True). This loses the structured error code on the wire — clients cannot distinguish error types without parsing the message string.

The existing UrlElicitationRequiredError (a subclass of McpError) already had a re-raise bypass, but the parent McpError class did not. The v2 McpServer on main already handles this correctly with except MCPError: raise.

Fixes #2770

How Has This Been Tested?

• Added test_mcp_error_in_tool_handler_propagates_as_jsonrpc_error — verifies McpError propagates as JSON-RPC error with code preserved
• Existing test_url_elicitation_error_thrown_from_tool — confirms UrlElicitationRequiredError still works (subclass of McpError)
• Existing test_normal_exceptions_still_return_error_result — confirms regular exceptions still become isError:true
• Full tests/server/ suite passes (503 tests)

Breaking Changes

Servers that intentionally raise McpError in tool handlers expecting it to be wrapped as isError:true will now get a JSON-RPC error response instead. This is the correct behavior per MCP spec — McpError represents protocol-level errors, not tool execution failures.

Types of changes

• Bug fix (non-breaking change which fixes an issue)

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

Two locations fixed:

1. src/mcp/server/lowlevel/server.py — the call_tool decorator handler
2. src/mcp/server/fastmcp/tools/base.py — the Tool.run() method

Both now use except McpError: raise which subsumes the previous except UrlElicitationRequiredError: raise since it's a subclass.

[StantonMatt]

Checked this against head 60f8fc7.

Focused local run passed:

uv run --frozen pytest tests/server/fastmcp/test_url_elicitation_error_throw.py tests/client/test_list_roots_callback.py tests/client/test_sampling_callback.py -q -> 8 passed

I also ran a small low-level Server.call_tool() probe because src/mcp/server/lowlevel/server.py changes separately from the FastMCP path. In that probe, McpError(ErrorData(code=-32000, message="server fault")) reached ClientSession.call_tool() as McpError, while a regular ValueError("regular failure") still returned CallToolResult(isError=True). That covers the low-level decorator behavior I would have wanted checked here.