My understanding is those pauses are based on the 2003 Heroes Act.
https://crsreports.congress.gov/product/pdf/LSB/LSB10568
For those interested, this is a fairly concise summary of the history and legal basis for the student loan pauses.
There is also a section on Legal Issues and Considerations for Congress which explores issues relating to the pauses which would also apply to the issue of loan forgiveness and the Education Secretary’s authority to do it.