Success URL and checkout join
Stripe already knows the money. Motif only needs to know which visitor owned the session.
Checkout Sessions you create
Keep Stripe's default placeholder on success_url:
https://yoursite.com/thanks?session_id={CHECKOUT_SESSION_ID}
{CHECKOUT_SESSION_ID} is Stripe's literal token. Do not replace it with a value from your database. When the customer lands on that page, the tracker reports the pair once per session id.
Payment Links, Buy Buttons, Pricing Tables
The tracker stamps client_reference_id with the visitor id before checkout. You do not add that parameter by hand unless you already set it; a value you set wins. Pricing Tables still need checkout_started from your code because their checkout-only click is not reliable to observe.
Identify is a different join
identify stitches the same person across browsers after login. It is not a payment. Call it with the stable app id, never an email.
window.motif?.identify(currentUser.id)