Sorry, there is a bit more to it, it should be called on the stripe object:
type stripe
@module("stripe") @new
external make: string => stripe = "default"
@val
@scope("checkout.sessions")
external createCheckoutSession: (stripe, {..}) => Promise.t<string> = "create"
let s = Stripe.make(Common.stripe_private_key)
// Does not work yet
let session = s->Stripe.createCheckoutSession({ "key": "value"})