Is the US set up such that the executive can do anything they want unless the legislative branch has put in restrictions?

I'm not that familiar with the structure of the US government, but I thought it was the opposite, and the executive has an approve list of powers rather than a deny list

There are laws and there are regulations. Laws are created by Congress and signed by the President.

Most of the time, laws are very vague and the specifics of the laws - the regulations - are written by government regulatory agencies. The president appoints heads of the regulatory agencies that are approved by the Senate (upper house).

Congress can pass a law that overrides a regulation or it can be struck down by court.

So the President by himself has limited power but he has a lot of influence over regulatory agencies based on who he appoints.

That isn’t very reassuring. He shouldn’t have had the power to unilaterally make this decision in the first place. While the legislature might have not passed a law that overrode his decision. I doubt they would have passed a law saying it was permissible.

The executive branch has the power to execute laws and regulations. I think what they're doing here is choosing to execute a law/regulation that they should've waived due to the pandemic.

That's why it's not necessarily an overreach, but instead just an inhumane choice to not take special circumstances into account when choosing to execute a particular regulation.