What is a recommended authentication architecture for a front GUI app that I want to control but that will be used by others to control their servers?

I have a front end (WEB GUI) app that I designed (Python for now + JavaScript in the future) that I use to access a controller, it uses REST APIs.

I want to publish this app in the cloud so that others could use it.

The biggest issue I am seeing is the security side as the app needs to authenticate with the remote server (a controller itself) and start sending tasks to the controller that will translate that in internal REST APIs to control for processes on downstream servers

Is there an authentication flow that will guarantee the owners of the controllers that I (the publisher of the front end) do not intercept the authentication flow and I gain unwanted access to their servers ?

My idea is to use a two steps authentication/authorization process like below. Is there a better way?
Please edit this diagram if you have suggestions
enter image description here

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Author: MiniMe