Plaid is one of a world leading open banking platform. Another one is TrueLayer.
As I understand it, when you use an open banking service like Plaid, TrueLayer, what you are actually doing is to give permission to the service to access your bank account information. It does not save your details. This information is then passed securely to the service via APIs.
It is understandable to worry about your detail when you use it for the first time. But whether you like it or not, it is the future of Banking. The Banking system will be moving to the direction of open Banking Platform to allow instant transfer between accounts. Also it is preferable by the government as it is much easier for them to detect money laundry when all of your transaction stay in one platform. So get ready for it, embrace it.