the iPhone 12 and I have the iPhone 13. Since the last update both of our phones shows no internet connection.
Check the range of the mobile network on both iPhone, see this Apple article: If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
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Check also the Wi-Fi network, see the following Apple articles:
Connect to Wi-Fi on your iPhone, iPad, or iPod touch
Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network
If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support
Recommended settings for Wi-Fi routers and access points
Recommended settings for Wi-Fi routers and access points - Apple Support
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If you need help with your Wi‑Fi password
If you need help with your Wi‑Fi password - Apple Support
If they are On, turn Off Hotspot & VPN.