The claim is usually made without specific citations. The few studies I'm aware of show correlation between mental health issues and phone use, but don't show which way the causation runs. It's just as plausible that mental health causes more phone use, yet these message boards always like to blame the phone for the mental health issues.

You’re not going to overdose from using your phone too much, or die from withdrawal if you suddenly stop using your phone, so that seems like a stretch.

Phone addiction is not identical. In some aspects its similar but in most others not.