Summary

When an SSE client connects with a custom path (e.g., /api/v1/custom/sse), ensure the endpoint URL maintains the same base path structure but with /messages instead of /sse. This fixes issues where custom endpoints were getting collapsed to the root path.

Problem

The SSE client was not preserving custom paths when constructing endpoint URLs. When a client connected to a server at a custom path like /api/v1/custom/sse, the endpoint URL would be constructed without preserving the custom path, resulting in POST requests being sent to /messages instead of /api/v1/custom/messages.

Solution

Modified the endpoint event handler in the SSE client to:

1. Check if the original connection URL contains a custom path
2. Extract the base path (removing the /sse suffix)
3. Apply the base path to the endpoint URL with /messages suffix

Testing

This PR makes the failing tests from #439 pass. The tests verify that:

• Custom paths are preserved when constructing endpoint URLs
• Multiple levels of paths are handled correctly
• Query parameters are handled appropriately

Related Issues

• Should fix Incorrect URL in sse.js when providing a custom path inspector#313
• Should fix Routes other than root ("/") for remote MCP servers don't seem to be supported. inspector#296
• Tests demonstrating the issue were added in Add failing tests for custom endpoints #439

Test Plan

• All existing tests pass
• New tests from Add failing tests for custom endpoints #439 now pass
• No breaking changes to existing functionality

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