Can not open links in email or text message on iOS 16.4

If you have an add-on VPN client installed, remove that, force restart, and try again.

If you have iCloud+ Private Relay enabled, disable that, force restart, and try again.

… Force restart iPhone - Apple Support

… About iCloud Private Relay - Apple Support

There have been a couple of updates since iOS 16.4. See if iOS 16.5 works better.