Could you please share a bit more about the scenario?
When users use this App for the first time in a new browser that you have never used before, the App would need them to sign in with their own credential to generate a connection for each of them, it should be only for the first time App usage in a new browser, if every time the user would need to sign in for the custom connector when using the App, then please consider update the App with an existing App owner.
Further, you should notice the browser issue in this situation, if you have already had an account/permission in the current browser, every time you open the shared app using the URL, it navigates you to the app directly.
Therefore, if you want to enable the auto sign in, please make sure that the browser they used to log-in the app already has kept the account before.
Sum it up as below:
1). Log-in in a new browser that never used, sign-in screen is required.
2). Log-in in a browser where you have already had an account/permission before, login will be automatic.
Ensure that it is not the first time they log-in using the account that is for the Power Apps App.