One of the other answers, by @Marco, has a negative score, and that is the one that I ended up preferring:
exiftool -b -PreviewImage IN.ARW > OUT.jpg
As pointed out in the comments, this has the disadvantage of not preserving the full resolution of the image. On my 14-year-old camera, the preview image extracted by ExifTool is 1616 x 1080, not quite the resolution of my monitor, but good enough for a web page. The other option for me, since I didn't want to use proprietary software, was @xiota's suggestion to use the command line interface of a GUI tool. The tool that I had been using is DarkTable, and the command-line is very simple:
darktable-cli IN.ARW > OUT.jpg
Perhaps for the future, I should read the user's manual and try to get the camera to save high-resolution JPEGs, but for my immediate needs, the
exiftool extraction option produced a suitable resolution and far superior colors.
It's unfortunate that, at least in my case, the DarkTable default output is so much lower quality than whatever the software in the camera is producing. However, I guess Sony put a lot of work into their software.
I decided to post this additional answer, because I figured I'm not the only web user who is willing to sacrifice resolution for color quality, and I wanted to make sure that the Marco's answer didn't get ignored or deleted.
Output of DarkTable (originally 4288 x 2856):
Output of ExifTool (originally 1616 x 1080):
Which one would you want to see on a web page?
Also, before you downvote this answer, note that the OP asked for:
"software (for Linux, eventually Windows) that helps me to have similar effect like auto in my camera (convert arw into jpeg)?"
(Check. This software produces an identical effect to that of the camera's firmware, because it is extracting the output of that firmware.)
"I want software to do that and I want to have jpegs as good as camera can process"
(The jpegs extracted by
exiftool are lower resolution than the camera can process - but aside from that, the quality is the same, because they came from the camera. Other answers produced inferior output for my use case)
"I want software that can choose proper settings like the camera does."
(In one sense,
exiftool is not choosing the settings; in another sense, it is choosing exactly the same settings as the camera...)
Update: One commenter expressed concern about the compression quality of the preview image. I don't think there's any reason for Sony to use a low quality compression for a preview image. The goal is to have an image that looks good on a small screen, and this is achieved with good compression but lower resolution.
To estimate the compression quality that my camera uses for previews, I used ImageMagick's convert tool:
convert IN.jpg -quality 96 OUT.jpg
I adjusted the quality until the size of the input and output was the same, in this case 508k. This corresponds to a quality of 96 which seems fairly high to me.
For comparison, the RAW image file is 13M, so the preview is adding less than 5% to the file size.