### Check for existing issues

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

### What happened?

An `org_admin` user (configured via `LiteLLM_OrganizationMembership` with `user_role = "org_admin"`) receives `401 Authentication Error` when calling `POST /team/update`, even though `/team/update` is listed in `LiteLLMRoutes.org_admin_allowed_routes` and the endpoint's own authorization check (`_verify_team_access`) correctly handles org admins.

The root cause is in the **proxy auth pipeline**: `non_proxy_admin_allowed_routes_check` rejects the request before the handler runs because the org-admin route-gate helper requires the request body to contain `organization_id`, but `UpdateTeamRequest` makes that field optional and the typical caller passes only `team_id`.

The same gap likely affects `/team/delete`, `/team/block`, and `/team/unblock`, which also rely on `_verify_team_access` and are not in `self_managed_routes`.

## Root Cause Analysis

### The bug: `_user_is_org_admin` returns False when no `organization_id` is in the request body

In `litellm/proxy/auth/auth_checks_organization.py:142-180`:

```python def _user_is_org_admin( re…