Looking through the API documentation for Notion, they have a very detailed step-by-step guide, on how to implement authorization to the API, using OAuth.
This would provide the flow we have all come to enjoy, where the end-user simply clicks a link, a page opens like the one in your screenshot, and they can log in, and grant access to their account.
The API documentation explains all this very well, so it should be relatively simple to implement this into your Anvil app.
Be sure to read through the documentation in details, as they provide some key points, on how to store the API tokens of your users.