I'm also on Fedora; make sure to follow the setup guide completely. There are a few commands it gives you that might improve battery life. Also, I was able to shave a few watts off of my 12th gen's idle power draw by setting the display to 48hz instead of 60. Be aware that your IO modules also use power, with the storage, Ethernet, and video output modules being the most demanding. If you aren't using any of those very frequently, consider swapping it out for a USB port. I run 2 of each USB port with HDMI and Ethernet modules stored in my backpack in case I need them.
I'm also on Fedora; make sure to follow the setup guide completely. There are a few commands it gives you that might improve battery life. Also, I was able to shave a few watts off of my 12th gen's idle power draw by setting the display to 48hz instead of 60. Be aware that your IO modules also use power, with the storage, Ethernet, and video output modules being the most demanding. If you aren't using any of those very frequently, consider swapping it out for a USB port. I run 2 of each USB port with HDMI and Ethernet modules stored in my backpack in case I need them.