I've heard this talking point before, and it's really silly to frame it as shenanigans somehow because of the timing, rather than elected officials enacting popular policies that the voters want.
There is a body of actually elected officials whose job is to create legislation to enact public policies. The FTC is neither elected nor capable of creating legislation. This is an overreach of their power and will likely be ruled as such in court.
The same thing happened with Roe; it is not the job of the Supreme Court to enact public policy. That is for the legislature to do. If you talk to anyone in law, they will tell you that, regardless of their personal opinion on abortion, Roe is perceived as one of the worst court rulings ever because it was specifically designed to “legislate through the court”. Here we are in the same position again, with a non-legislative body enacting public policy; we don’t learn.
"Under this Act, as amended, the Commission is empowered, among other things, to (a) prevent unfair methods of competition and unfair or deceptive acts or practices in or affecting commerce; (b) seek monetary redress and other relief for conduct injurious to consumers; (c) prescribe rules defining with specificity acts or practices that are unfair or deceptive, and establishing requirements designed to prevent such acts or practices; (d) gather and compile information and conduct investigations relating to the organization, business, practices, and management of entities engaged in commerce; and (e) make reports and legislative recommendations to Congress and the public."
Noncompete acts are an unfair method of competition (see (a)), which Congress granted the FTC the power to define and restrict (see (c)). It is, quite literally, their job.
That's literally their job.