If you use multiple Apple devices signed in with the same Apple Account and have enabled Share Across Devices under Screen Time, your Screen Time settings and activity information are synchronised across those devices through iCloud.
This means that your App Limits, Downtime, and other Screen Time restrictions are generally shared across all devices associated with that Apple Account.
The good thing is that you do not have to manage Screen Time settings separately on every device. You can modify the App Limits, change Downtime schedules, or adjust other restrictions from any one of the devices signed in with the same Apple Account. Once the changes synchronise through iCloud, they will be reflected on the other devices as well.
In short: You can manage Screen Time settings from any one of your Apple devices, and the changes will be synchronised across your other devices, provided Share Across Devices is enabled and iCloud synchronisation is working correctly.
This makes managing Screen Time much easier, particularly when you use an iPhone, iPad and Mac.