There's no embargo for pet travel to the US. If your dog is eligible to (re-)enter the country with the current restrictions that were extended until the end of July 2024 in place and you have the paperwork to prove that, they'll transport him. A US dog that hasn't been in any high-risk country and which has all the required rabies vaccination documents is eligible to enter the country in any case.
It's all on the "importing dogs to the USA section on the "travelling with animals" website.

Email the LH service center ([email protected]) or use the feedback form on the website to clarify.