Keyboard Maestro Engine should use < 1% CPU when idle.
If it is using more than that (other than maybe just after launch), then it is not idle - either it is executing a macro, or perhaps performing condition checks for the editor.
Check what macros are running and quit the editor (or deselect all macros so no macro is showing).
If that doesn't resolve it, then use the Activity Monitor to get a sample and send it to me.
I didn't say anything about other macro apps, I said to check for running macros in Keyboard Maestro Engine. You can check in the Cancel menu in the Keyboard Maestro status menu.
As far as your Sample goes, I have no idea what is going on with that - it is spending all its time in Apple code, NSToolbarView layout, but I don’t think Keyboard Maestro Engine ever uses a toolbar anywhere. So I don’t have any idea why it is burning CPU on your Mac. I checked mine and unsurprisingly it is less than 1% while idle as expected.
From what you've described, you're having an issue with the beta version of macOS, not an issue with Keyboard Maestro.
With that said, I have a test machine running 27.2, and it's fine (other than an AppleScript issue that seems to be only affecting maybe two or three people). I displayed the Application Palette, launched 12 apps, and my total Keyboard Maestro CPU usage is 1.1%, sometimes hitting 2.5%.
As a general recommendation, I think you should flip this: Your main machine should always run the latest shipping OS, and your development machine should run the beta. You don't want some issue in a beta bringing down your main Mac. I can't imagine having my main Mac running a beta, given all the important stuff that happens on it...to have it break because of something in a beta would be very painful. Just my $0.02, though.
Then try the betas out in a sacrificial VM first, with the software (like KM) that you need, to make sure everything you need to be productive is working before you put it in your main. Or use the beta-running VM to test your developed software.
There is no one good answer to this, I'm afraid -- running betas on a production machine is always a risk.
Totally understand -- but it was what was required to fix a beta/KM issue in this thread. So prepare yourself, in case the next update doesn't fix the problem.
Edit to add:
It would be worth checking the Engine log file, if you haven't already. Quit the Engine, run tail -f ~/Library/Logs/Keyboard\ Maestro/Engine.log in Terminal, launch the Engine again and see if anything weird shows up -- perhaps an old Library item not resolving, a macro that runs an async AppleScript querying the Engine, or similar.
If you are having no probs under 27.2 then perhaps it is not a beta issue but something else.
I actually have quite a few things running on my Mac so a conflict is always possible.
It is just strange how it manifests. All conflicts I have encountered before present as features or apps not functioning, not excessive CPU usage of another app/process.
BTW I have not had any other issue with the betas I run. Occasionally an app will need to wait until an official release before I can use it again, but this is rare and never on an essential use app.