Rough roads
My hands and shoulders get sore quite easily. (I'm in my upper 60s.) I ride two kinds of rough roads:
Buzzy chip-seal. This is more of an annoyance. My 28mm GP5000 at low pressures help a lot here.
Or jarring expansion joints, bad patchwork, and thick tar strips. Ow, these can be hard on hands and shoulders. Riding in the drops helps here: Leaning over a bit more, my core is helping support the weight, my arms are bent to help reduce shoulder soreness, and the pressure is spread evenly across my whole palm. The 28mm tires probably help, but they can't fully absorb shocks like this. (I rode some flexible 38mm tires at 40 psi on another bike. Those were very nice on choppy roads, and made chipseal buzz disappear.)
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Bike fit
The bar, hood, and saddle positions on your bike photo wouldn't work for me. Way too much pressure on my hands from the saddle tilt. And bent wrists from the hood position. (Perhaps the camera angle exaggerates these angles, I suppose.)
Your bike:
Here's my bike setup. The bike and camera are both leveled, and the photo is shot at saddle height.
The green line is a horizontal reference.
Saddle:
I started years ago with the nose level. This works better, with the sit bone area level. No sliding forward. (I also see this a lot with leather Brooks saddle riders--nose up so the contact area is level.)
Bars:
A bit more than an inch drop to the top of the bars.
Hoods are angled up to even out the pressure across my palm and straight wrists. I have long fingers, so there's no problem with the reach to the brakes.
Drops are also angled to even out the pressure across my palm. The drops work great for me like this--I use them as just another comfortable hand position. In the old days, drops were only used for strong headwinds or control on fast downhills. Switching back and forth between hoods and drops is very good on longer rides.
I have to be careful not to ride pressing on the center of the base of my palm, which can aggravate soreness. This setup works well. And I tried lots of different padded gloves to find ones that have correct-for-me padding on the palms.
Saddle setup:
This fitter's video was very helpful. Saddles too far forward put too much weight on hands and shoulders.
It's an easy test to check saddle setup and position.
Saddle Fore Aft fit
Bar setup:
With bar tape off, I sit on the bike in a doorway for support.
First, the drops:
I start with the drops pointing approximately to the rear rim brakes.
I shake out my arms and hands to help get a neutral position, then reach for the drops. I want the whole palm to contact with minimal wrist bending. Adjust the bar angle a bit, and check again.
Once the drops angle is set, the hoods are adjusted similarly, trying for straight wrists and even hand contact.