What type of visas do you have?
No, there's no issue at all in traveling to China for tourism or business. It is best to come to China within the scope of the visa though; i.e. business visa for business travel, etc.
Bring both passports, old and new.

(I wasn't even aware there was a US State Department advisory; what are they warning against? The "evil" Chinese regime? )

Many of us are traveling back and forth, China/USA without any problem whatsoever. In fact many of us did this throughout the pandemic ---> it's LOT easier nowadays!