Yes, it is possible to manage multiple stores with their own payment methods and associated bank accounts in Magento 2 using its built-in multi-store functionality. Each store can have its own set of products, customers, and sales, while sharing a common catalog.
To display a general catalog with all the products of all the store's catalog, you can create a new website in Magento 2 and assign all the existing stores to this website. This will allow you to share a common catalog across all stores, while still maintaining separate payment methods for each store.
Regarding your question about what happens if products from different stores are added to the cart, Magento 2 will create separate orders for each store and assign the corresponding payment method for each order based on the store from which the product was added. This ensures that each store receives payment for the products sold through their store.
There are also several marketplace extensions available for Magento 2 that can help you manage multiple stores and their associated products and payments, such as the Multi Vendor Marketplace extension by Webkul.