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No need to do any "submit", your data always lives on the server. You need to let go of some of the mindset that comes with regular web development. When creating apps with Vaadin, try to think of it as more like developing a desktop application, where you don't need to care about any client-server communication.
So to save your data to a database, just use whatever you know on the server side, e.g. connect to your database, make an SQL statement.