Hi, I'm John! I will help you with this.
When signing in, make sure to click "Send notification" this should trigger the Authenticator app to show the pop-up.
If there's no pop-up notification, expand the notification area in your phone and check for any from Microsoft Authenticator "New sign-in request for your Microsoft account".
If you don’t receive the notification after clicking "Send notification", you can try troubleshooting the Microsoft Authenticator app using the steps in this guide from Microsoft: "Troubleshoot problems with Microsoft Authenticator" https://support.microsoft.com/account-billing/troubleshoot-problems-with-microsoft-authenticator-a3a74493-566b-4c2e-b949-a2789bac0fd3
Let me know how it goes. Or if you have any further questions or concerns.
Click "Add comment" to let me know.
Regards,
John J.D.