I went back looking through my LR catalog at all my Sony RX !0 IV images ( ~ 1000 ) and while I don't like many of them, that is frequently my fault - poor composure, lousy lighting etc. I had a feeling that they would be noisy at high ISO due to the small sensor, but I found a number of images at ISO 3200, and even 6400, that I felt looked rather nice for the very dark circumstances and would be quite useable for modest prints up to 16 x 20 or so.
I rediscovered a secret I found accidently - the High Speed Frame rate is so high that I was able to create a a couple pano images ( merged multiple frames 6-9 ) of the Blue Angels in formation in flight as they blew by overhead in a high speed pass.. I created a 6 to 8 frame pano of 6 jets airplanes with no single image with all the airplanes in it. I have never thought of trying to merge multiple images of airplanes in high speed flight, but the high speed frame rate at 1/1000th shutter speeed allowed me to merge the images in LR.
I looked at exposure too, @Chris I find LR in auto mode - Apple-u keyboard combination in the Develop module - does frequently want to add +0.7 to +1.25 stops of positive exposure, but I think LR tends to want to brighten images shot with my EOS bodies as well. I don't always like the results from auto Exposure as the shadows are lightened so much they take on an HDRish appearance and the image is a bit flat to greyish to my eye - but I grew up with Kodachrome and its black quarter tones. I wonder if this is what you are experiencing with your Sony images. How does the histogram on the camera body look for your exposures?
I did regain a bit of faith in the quality of my Sony RX10 Mk IV images and I will pursue its use some more. I still favor APS-C or larger sensors most of the time, but as a museum camera - even at high ISOs - the Sony produces capable results, The long lens will let one gather images they otherwise would not, but I find shooting people at the long end in front of vegetation or other backgrounds does not create a bokeh I favor very often.
It is a pretty large camera for its sensor size, which is significantly smaller than a m4/3 sensor. But I think its noise compares favorably to my m4/3 bodies at higher ISOs. I would be interested to hear other opinions regarding the noise in the Sony versus m4/3 bodies
Here is about 1/2 frame crop from my Sony RX10 Mk IV at ISO 3200 in late soft light chasing short eared owls last year