where do I find cycle count in the new System Settings

It is easier to launch the Apple System Profiler by Option-clicking the Apple menu and selecting the first item. Click on "Power" on the left pane and you will get the battery details on the right pane. This information has been available at this location for as long as I can remember unlike the System Preferences/Settings app which has been in constant upheaval over the last few years.

There is a long path there ...

System Settings > General > About > [scroll down to] System Report > Power > Battery Information