### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

LiteLLM’s /mcp/ endpoint has two latency issues:

1. tools/list unnecessarily fetched initialization instructions from upstream MCP servers, even though instructions are only needed during initialize. 2. LITELLM_MCP_TOOL_LISTING_TIMEOUT cancelled slow listings at the configured deadline, but still waited for MCP SDK cleanup. A five-second timeout could therefore take much longer to return.

### Steps to Reproduce

1. Configure LiteLLM with multiple MCP servers, including one slow server. 2. Set LITELLM_MCP_TOOL_LISTING_TIMEOUT=5. 3. Send an unscoped tools/list request to /mcp/. 4. Observe that upstream initialization requests are made and the response can take significantly longer than five seconds.

### Relevant log output

```shell

```

### What part of LiteLLM is this about?

_No response_

### What LiteLLM version are you on ?

v1.88.0

### Twitter / LinkedIn details

_No response_