“Is there an objective way to measure metabolic state and aerobic capacity? What procedures or labs are done that measure it?”
Here’s is what I need to know before answering this:
To measure your metabolic state you just have to look at what you’re eating, your waist circumference, some family history, and your overall symptoms.
Can you get more granular? Sure! I can measure your mitochondrial activity but is that valuable?
You could check your Tg/HDL ratio, check a serum HOMA-IR score, etc.
For aerobic capacity, you can look at how much you’re exercising or how active you are. I will bet my laptop that your current activity level is the strongest predictor of your aerrobic capacity.
You can also get your VO2Max, RHR, HRV, and heart rate recovery.