#23348 [Bug]: Multiple MCP integration issues: tool registry lookup, OpenAPI spec_path fallback, and MCPServerTable diagnostics
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate.
### What happened?
While integrating and using MCP features in litellm, we have encountered three issues that impact usability and robustness:
1. **Double-prefix error in MCP tool registry lookup** **Problem:** When requesting a tool from the MCP registry, the code always prefixes the tool name with the server name. However, sometimes the tool name is already prefixed (for example, when called from the MCP inspector UI). This causes the lookup to fail, as the registry searches for a double-prefixed name that does not exist. **Impact:** Tools registered with a single prefix cannot be found if the request already includes the prefix. Error message: "OpenAPI tool ... not found in registry"
2. **OpenAPI tool preview fails if spec_path is missing in the request** **Problem:** When adding or editing an MCP server via the UI, sometimes the request sent to the backend does not include the spec_path (the path to the OpenAPI spec), but does include the server_id. The backend currently only checks for spec_path in the request, so if it is missing, the preview of avai…