No, there are no federal or state regulations requiring establishment and use of an Employee Assistance Program at the time of this writing in 2021.
While it is not mandatory, it is popular. The Workplace Outcome Suite (WOS) Annual Report 2020 (https://wellbeing.lifeworks.com/wp-content/uploads/2020/09/WOS-annual-report-2020-part1-.pdf) reports that “31% of small employers had an EAP in year 2019; followed by 66% of medium size companies and 84% of larger size companies. Almost eight of every 10 public sector employers had an EAP as well (78%). However, across all types and sizes of employers in the United States, only about half had an EAP in 2019 (54%).”