If a user wants to change a connection (e.g. an API key) he/she has to create a new connection and set it in all the scenarios and all the modules using that connection.
The same for OAuth connections - allow to change the attached account or enforce reauthorize.
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UPDATE: Reauthorize connection button on Connections page is shown for OAuth2 connections. You can use it for changing of connected 3rd party account instead of creating a new connection and switching it in all your scenarios. Of course, you can use it for refreshing your connection if the connection is no more valid.