### The Feature

Operators running multiple LiteLLM proxy environments (dev / staging / prod, or regional clusters) currently have no first-class way to export the proxy's UI-managed state into a declarative artifact that can be re-applied in another environment.

`config.yaml` is declarative for everything sourced at startup, but UI- and API-driven state — teams, organizations, virtual keys, credentials, MCP servers, agents, access groups, models added via the dashboard, and a chunk of `general_settings` (alerting, SMTP, etc., persisted into `LiteLLM_Config`) — lives only in the database. There is no single endpoint or CLI that emits all of that state in a redeployable form.

### Motivation

Multi-environment promotion ("apply what's in staging to prod") is a common operational need, especially for regulated deployments where every config change has to be reviewable and reproducible. Today this requires either:

1. Hand-stitching a backup script across the per-resource admin endpoints (`/team/list`, `/organization/list`, `/key/list`, `/credentials`, `GET /v1/mcp/server`, `GET /v1/agents`, `/v2/model/info`, plus the access-group endpoints and `/config/list` / `/ale…