My iphone 12 mini somehow added the country code (US) to all my contacts, and now I can't make calls.

You can change the country format for addresses and phone numbers using https://www.icloud.com

Note: These changes apply only to Contacts on iCloud.com. For other email accounts which hosts your contacts read the email account documentations.

1. Click the Action pop-up menu  in the sidebar, then choose Preferences.
2. Choose a country from the Address Layout menu.
3. To have Contacts automatically add hyphens and other symbols in phone numbers, select “Automatically format phone numbers.” If you want to be able to enter phone numbers in more than one format, don’t select this option.
4. Click Save.

Watch this GIF Below

For Gmail Contacts, see the pic below

When you look deeply you will find that Contacts are neither stored on an iPhone nor on SIM. They are synced to an email account that you may have added and enabled Contacts. It could be Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other email client server.

When you enable Contacts in any of the email accounts they are displayed to you through the Contacts App. When you edit these contacts on an iPhone they are ultimately edited on the client-server.

Please see the pic below for a better understanding...