I thought I would deviate from discussing the Sony battery to talking about the Sony RX100 III in general. I really like the camera, and I find it easy to shoot with. My goal was to get my camera weight way down due to back surgery last fall, and this camera with my little Osprey carrying bag reduces my weight to 15 ounces, instead of the minimum 2 pounds I use to carry with my Micro Four Thirds camera/lens into the backcountry(not including tripod). I know the camera is not going to give me what a dslr with great lenses would, but I was after a good quality compact camera, and I think this one suits my needs right now. I carried it for the first time on a trip July 25-27.
Some of the things I like the most:
Built in viewfinder plus a pretty good LCD screen.
Shooting in RAW: the processing time is very fast when you shoot a burst, or bracket exposures, compared to many other compact cameras
Custom settings: I found it easy to set up 3 typical scenarios for shooting, and not have to fiddle around much with camera menus after that.
The lens is fast. I can vary ISO up to about 800 to change exposure levels without worrying too much about a drop off in quality.
24mm wide angle is great

A couple of things I am not sure about: the battery life seems short. When I take a long trip, I don't want to have to take a bunch of spare batteries, or a solar charger. One spare battery would be no big deal, but I went thru 2 batteries in 3 days. Perhaps this will improve. Also, I had the camera on at times viewing images, not just snapping shots, and turning it off. According to the specs, if using the viewfinder, which I do, the battery is only rated for 230 shots.
Filter system: The only adapter available for filters like a polarizer or graduated neutral density seems to be an adapter that you glue on, or it sticks on. Seems like a weak design for such an expensive camera. The Sony has a built in ND, but it is not a blanket solution for high contrast Sierra scenery.
The third issue: I wish the camera was cheaper! But I look at it like buying lightweight backpack equipment, getting weight down can cost a lot of $$.
All in all, I am very satisfied with the camera. Most cameras I have carried into the backcoutry, there has been some kind of compromise to save weight. I like the quality of the photos. I think a shooter with more ability than I could get a lot more out of this camera.