Hi Massimo,
Based on what you described in your original post regarding Screen Time, we recommend that you try the steps in the link below.
Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support
To perform the recommended troubleshooting steps via the link above, complete the steps in the section titled "Turn on Screen Time."
1. Go to Settings > Screen Time.
2. Tap Turn On Screen Time, then tap it again.
3. Select This is My [device] or This is My Child's [device].
After you turn on Screen Time, you'll see a report showing how you use your device, apps, and websites. If it's your child's device, you can set up Screen Time and create settings on their device or you can use Family Sharing to configure your child’s device from your device. After you set up your child’s device, you can also use Family Sharing to see reports and adjust settings from your device.
With Screen Time, you can also create a dedicated passcode to secure settings, so only you can extend time or make changes. Make sure to choose a passcode that's different from the passcode that you use to unlock your device. To change or turn off the passcode on your child's device, go to Settings > Screen Time and tap your child's name. Then tap Change Screen Time Passcode or Turn Off Screen Time Passcode, and authenticate the change with Face ID, Touch ID, or your device passcode.
We recommend the steps above to ensure you have set up Screen Time correctly.
If you're still experiencing the same issue, follow up with the steps in the section below titled "Manage Screen Time settings."
Go to Settings > Screen Time. Then tap See All Activity, select a category in the list below and set limits. You can manage these settings with Screen Time:
Downtime
When you schedule downtime in Settings, only phone calls and apps that you choose to allow are available. Downtime applies to all of your Screen Time-enabled devices, and you get a reminder five minutes before it starts. If you set a Screen Time passcode, Downtime includes an additional setting: Block At Downtime. When you choose this setting and you click Ask For More Time when Downtime starts, entering the passcode allows you to approve the app for 15 minutes, an hour, or all day. Child accounts can click One More Minute once, or click Ask For More Time to send their request to the parent account for approval.
App Limits
You can set daily limits for app categories with App Limits. For example, you might want to see productivity apps while you're at work, but not social networking or games. App Limits refresh every day at midnight, and you can delete them any time.
Communication Limits
Control who your children can communicate with throughout the day and during downtime. These limits apply to Phone, FaceTime, Messages, and iCloud contacts. This is also where you can decide and manage which contacts are available on an Apple Watch paired through Family Setup. Communication to known emergency numbers identified by your iPhone or Apple Watch cellular carrier is always allowed. You need to have your iCloud contacts enabled to use this feature.
Always Allowed
You might want to access certain apps, even if it's downtime or if you set the All Apps & Categories app limit. Phone, Messages, FaceTime, and Maps are always allowed by default, but you can remove them if you want.
Content & Privacy Restrictions
You decide the type of content that appears on your device. Block inappropriate content, purchases, and downloads, and set your privacy settings with Content & Privacy Restrictions.
Please let us know the outcome after giving the above steps a try.
Thanks for using the Apple Support Communities.
Cheers!
