Well of course, JPEG artifacts aren't necessarily going to be easier for png to compress. You need to make modifications designed for png's algorithm. There are some tools that do this:

https://pngmini.com/lossypng.html

https://pngquant.org/

https://tinypng.com/

The resulting png's are much smaller. Though not necessarily as small as JPEG, it's in the same ballpark.

pngquant is pretty awesome, especially for screenshots. For example a screenshot of my terminal running dd, it reduces the size from 88K to 17Kbytes.