It's something current federal law does and has done for decades. A person who is involuntarily committed to undergo inpatient treatment at a mental health facility by a court of law is classified as a "prohibited person" and cannot own or have access to firearms.

Source link: https://www.atf.gov/firearms/qa/are-there-persons-who-cannot-legally-receive-or-possess-firearms-andor-ammunition

The catch is that a person cannot be deprived of any right without due process - typically a literal day in court. Therefore an individual with mental health problems that have not caused enough trouble to land them in front of a judge can't be declared a prohibited person.