Free T3 below midrange can affect the results of TRT, I would start TRT in isolation and see how you progress, if you respond well to TRT that would mean your body is happy with the thyroid hormones being produced.
You have to understand how doctors are trained, they are taught to treat the reference ranges and ignore the patients symptoms. So within the normal ranges doesn’t always mean symptoms will be present the moment you dip below ranges, often symptoms will occur in the lower normal range for testosterone and thyroid.
Most doctors would say a Free T3 of 2.0 is normal and no treatment is needed, yet the moment you score 1.9, now that take action as if there’s a sharp line that when crossed symptoms are present. It’s robotic to think like this and replaces the need for analytical thought and critical thinking.
It’s how doctors can see 20-30 patients in an 8 hour shift.