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is the Subscription API (https://stripe.com/docs/api/subscriptions) part of Stripe Billing and thus subject to the additional fee?

yes, as we found out through the email. Even if you send invoices, they will also take a 0.5% of those!

AFAICT - Yes

[1] In Stripe's API, the subscriptions section is nested under "Billing"

[2] https://www.stripe.com/billing is all about handling subscriptions through Stripe