Under Trump, could a legal action for Writ of Mandamus be used

to force an agency to do its job?

Example: the Office overseeing Medicare cuts benefits by 50% despite funding being available.

Could a Medicare beneficiary/group of beneficiaries/organization (e.g., AARP) sue that office to compel it to do its statutory duties?

Writ of Mandamus was the device used in Marbury v. Madison, when Jefferson refused to seat an individual to his office, appointed by outgoing President John Adams. SCOTUS made Jefferson seat him.

A (writ of) mandamus is an order from a court to an inferior government official ordering the government official to properly fulfill their official duties or correct an abuse of discretion. See e.g. Cheney v. United States Dist. Court For D.C. (2004). According to the U.S. Department of Justice, "Mandamus is an extraordinary remedy, which should only be used in exceptional circumstances of peculiar emergency or public importance."
https://www.law.cornell.edu/wex/mandamus#:~:text=A%20(writ%20of)%20mandamus%20is,United%20States%20Dist.