Sadly, the small Control Strip the Touchbar of macOS shows is only customizable to a small degree. Buttons like Next and Previous cannot be added to show, when only the smaller size Control Strip is visible.
However, you can easily edit the contents of the file at ~/Library/Preferences/com.apple.controlstrip.plist with e.g. Xcode:
Just change the MiniCustomized Section to what you want to have in the small version of the Control Strip.
You can find all the possible values in the
This way, you can e.g. setup this Media Player Control Strip:
After changing the file, save it and reboot to make your mac load the changes.