MCP SDK Path Handling Bug for Subpath Servers

[tobegit3hub]

Issue:
Clients (Inspector/Cherry Studio) fail to connect when MCP Server uses a subpath (e.g., http://domain.com/subpath/sse). Root paths (http://domain.com/) work normally.

Reproduce:

1. Start MCP Server at http://domain.com/subpath/sse
2. Client connection fails with error:
   Error POSTing to endpoint (HTTP 503): no healthy upstream

Cause:
In sse.ts#L146, new URL() discards the subpath from the server URL. Example:
Request to /messages/ becomes http://domain.com/messages/ instead of http://domain.com/subpath/messages/.

[Njuelle]

hi @tobegit3hub ,
here is a PR that fix this issue, do not hesitate to check if it fits your needs and let us know :)

[tobegit3hub]

Thanks @Njuelle . I'm not sure if it is a issue in sdk or not since other MCP Servers which are not implemented with FastMCP do not have this issue.