Road bike drag decrease with bulky backback I'm about to increase my daily commute from 5 km each way to 10 km each way. I've been using a MTB converted to a commuter for years. Given the extra distance, regular evening head wind, and aging body, I'm considering getting a road or cyclocross bike or for better efficiency.

I usually commute with a large backback full of clothes, towel, laptop, lunch containers, etc. My question is, would the aerodynamic gain of switching to a road bike be negated by the backback? If so, would panniers or some other solution be better in terms of drag?
Your very question has actually been answered by GCN (below) and Specialized and has been partially answered in  What's more aerodynamic on flat bars: backpack or pannier?
Essentially the in order of fastest to slowest:

Large saddle bag (i.e., bike packing bags)
Back pack
Pannier

By far the panniers will be the slowest option as you are hanging the bag out in the full wind.  Backpacks are pretty fast, but do affect wind transferring over your back.  If you don't have a lot to carry bike packing bags are the fastest option as they are tucked away the most.
Over the last 2 years I have switched completely to bike packing bags and a fast road bike for my 45 km commute (2 way) and probably save close to 10+ minutes per day.
One thing not tested in the videos is a front roll bag.  I have good luck with that setup as I think it acts a bit like a wind fairing for your upper legs which do cause a lot of air disturbance.
What's The Best Bag For Commuting By Bike? Saddle Bag Vs. Panniers Vs. Backpack

Screen capture with the actual data with a suspect y-axis scaling... Come on Emma your are a PhD scientist!