The HomeConnect app for iOS no longer indicates that a profile has been paused (when it actually is) and therefore I can't unpause the applicable profile without going into the settings and adjusting the profile's downtime. I'm on iOS 16.6.1 and an iPhone 12.
That is strange that you are unable to see the pause icon to indicate that a profile or device has been paused so that you can unpause it. Did this issue just recently start occurring for you? I tried it on my iPhone 12 Pro with iOS 16.3.1, and I was successfully able to pause and unpause. I created a new profile as well, added some devices to it, and was also able to pause and unpause.
Can you try uninstalling the application from your phone and reinstalling it, then testing it out?
Can you also try deleting the profile and then creating a new one to see if that works?