Resolve already has a few built in.
The "Beauty" plugin is what looking for, if you're trying to do what Photoshoppers sometimes call the "frequency separation" method of skin refinement. It controls blur/sharpness based on different detail thresholds. In Resolve, you'll want to select "Advanced" from the dropdown menu to get access to the Hi/Low rolloff sliders, although they have unusual names ("Smoothing threshold", "Diffuse Lighting", etc, which doesn't actually have anything to do with Lighting).
The image you posted looks like what "Beauty" does, but when you talk about Davinci's Midtone Detail slider, you're looking for something more like "Contrast Pop."
Contrast Pop works similarly, but instead of letting you blur/sharpen based on a detail threshold, it lets you adjust midtone detail based on adjustable thresholds. Again, the plugin name is bad, and I didn't discover it for a while because the name was so distasteful, but It's probably close to what you're looking for, and works well in conjunction with "Beauty".
"De-flicker" also lets you qualify the plugin's application based on a threshold, and then blends the image temporally, over a number of frames, in the chosen regions. It uses optical flow motion estimation to set the threshold, however, and might not work exactly like you need, but it might be worth a shot, depending on what you're doing.
Those are the three built-in ones that come to mind, and you could always roll your own, so to speak. If you google "frequency separation" and watch some photoshop videos, the technique can be achieved with Resolve nodes fairly simply, and adapted however you see fit. Once you've got a setup that works, save it as a "power grade," and it'll be accessible from all of your new projects. No need for a plugin.