Hey there Vide98,
Thanks so much for using Apple Support Communities.
We want to help you customize Screen Time so that it's working exactly as you like. While it's not possible to allow all websites through your Safari "Allowed Websites" list, you could potentially add some of the websites that you use most often so that they are excluded from any Screen Time restrictions that you have in place on that device. This article goes over how you would add websites to that exclusion list: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support
Those steps are also included below:
Prevent web content
iOS and iPadOS can automatically filter website content to limit access to adult content in Safari and other apps on your device. You can also add specific websites to an approved or blocked list, or you can limit access to only approved websites. Follow these steps:
1. Go to Settings and tap Screen Time.
2. Tap Content & Privacy Restrictions and enter your Screen Time passcode.
3. Tap Content Restrictions, then tap Web Content.
4. Choose Unrestricted Access, Limit Adult Websites, or Allowed Websites.
Depending on the access you allow, you might need to add information, like the website that you want to restrict.
Another option would be to allow Safari entirely by making that an "allowed app" in your Screen Time settings. The steps for that are also included in the article above, but we'll include them below as well just to make things easy:
Allow built-in apps and features
You can restrict the use of built-in apps or features. If you turn off an app or feature, the app or feature won't be deleted, it's just temporarily hidden from your Home Screen. For example, if you turn off Mail, the Mail app won't appear on your Home Screen until you turn it back on.
To change your Allowed Apps:
1. Go to Settings and tap Screen Time.
2. Tap Content & Privacy Restrictions.
3. Enter your Screen Time passcode.
4. Tap Allowed Apps.
5. Select the apps that you want to allow.
We hope that this information is helpful.
Have a great day!