Charlestons - client_reference_id | Stripe Developers | Page 1

I don't think that that data is copied to the Subscription unfortunately. You might want to set this as metadata on the subscription via the subscription_data.metadata parameter https://stripe.com/docs/api/checkout/sessions/create#create_checkout_session-subscription_data-metadata

Stripe API reference – Create a Session – curl

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#Charlestons - client_reference_id