how to update password on authentication app

Question

Hi,
I recently had to update my password (couldn't remember it) and did so successfully and was able to get access into my email using the 2-step authentication (along with the new password).

But then I got this email from Microsoft after changing my password:

I had already setup this 2-step verification before I updated my password. I assumed this message was about the authentication app. When I opened that app, it directed me to a page where it automatically generated the password, with the instructions:

"Enter the app password below in the password field of the app or device that can't accept security codes. If you're not sure how to update your app or device with an app password, follow these steps."

I was confused by this since there was no password field below it, where I could enter this generated password. I also looked at the referred link on the steps it mentioned and it only stated this: "Enter this app password where you would enter your normal Microsoft account password in the application."

The only place I enter the password is when logging into the app. So I logged out of the app and tried to log back in using my email since that was the account setup on that app. Instead of entering my email password, I entered the generated password, but it rejected that. I was only able to get back into the app using my email password. So I'm still not getting where I'm suppose to enter this generated password.

The instructions given, did NOT help at all about where I'm suppose to enter this randomly generated password in the app. Please advise me where I'm suppose to enter this generated password because the instructions were insufficient.

Also if one has setup this authentication app to be "Passwordless sign-in enabled", does one really need to update the password?

Further, why does one have to update the password on this app every time someone updates their email password?