Thanks for the question. https://shopify.dev/apps/subscriptions/migrate/contracts describes migration paths to Shopify Payments for subscriptions. The instructions assume your current subscription payments are handled by Stripe. We (Shopify) don't have migration instructions for other payment providers.
One approach you might investigate is to move the Braintree payments to Stripe, then to Shopify Payments. You could check out this link as a starting point for your investigation.
Feel free to let us know if you have more questions.