### Check for existing issues

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

### What happened?

## Environment - litellm-database image 1.90.2 (confirmed same code path present on main as of 2026-07-04) - Deployed via the litellm-helm chart, Kubernetes - SERVER_ROOT_PATH=/litellm - Postgres-backed (DATABASE_URL), Redis cache - Auth: virtual key belonging to a team with an MCP-granting access group attached

## Summary When SERVER_ROOT_PATH is set to a single path segment (e.g. /litellm), the native MCP streamable-http endpoint always returns zero tools from tools/list — even for a key that is correctly authorized for one or more MCP servers. The REST convenience endpoints (/mcp-rest/tools/list, /v1/mcp/server) are unaffected and correctly return the full tool list for the same key at the same moment, which rules out any permission/access-group misconfiguration.

## Root cause `_get_mcp_servers_in_path()` in `litellm/proxy/_experimental/mcp_server/server.py` (~line 3020):

```python segments = [s for s in path.split("/") if s] if len(segments) >= 2 and segments[1] == "mcp" and segments[0] != "mcp": return [segments[0]]

This exists to…