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Nick here from Shopify. Really good question!
I looked into this for you and spoke to the financial services team about it directly. The financial services team mentioned that when using Shopify Payments, you can still go back and see payouts through it after you have changed to another provider. But regards to sharing customer information with a new payment processor, that definitely wouldn't happen or be available for security and privacy reasons. For example, Shopify Payments only has access to information from orders processed through Shopify Payments and the same would apply for other payment gateways.
I hope this helps and answers your question.
All the best, Nick