Create Connection

**mode** — for API-key-authenticated requests, mode is derived from the key type: `sk_test_*` creates development connections and `sk_live_*` creates production connections. Cookie-authenticated management requests still honor the request body's `mode` value. Production connections are created immediately, but remain non-operational until Stripe billing is completed. The response includes billing redirect details. **externalId** — your own identifier for this connection (e.g. your customer or user ID). Must be unique within your account. Once set, it can be used anywhere a `connectionId` is accepted, so you never need to store our internal IDs.