Keyboard Maestro back to version 4.x should operate fine in general on Big Sur and Keyboard Maestro itself has no known problems with Big Sur. Keyboard Maestro from version 9.1 is also native for Intel and Apple Silicon.
Big Sur probably continues to suffer from the variety of bugs and issues that Mojave/Catalina have, which are documented at:
As they are confirmed to still exist in Big Sur, I'll copy them below here.
XKey Devices do not work with Keyboard Maestro in Big Sur
There appears to be an incompatibility between Big Sur and XKey devices such that the "value" component of their key events is no longer 1-4 bytes (holding a number), but is inexplicably 32 bytes. PI Engineering are looking in to the issue, and hopefully so is Apple.
You will have to ensure you enable Accessibility for both Keyboard Maestro and Keyboard Maestro Engine. If you have any troubles with accessibility (eg typing keystrokes, selecting menus, copy/paste, etc), you need to toggle the accessibility permissions (System Preferences, Security & Privacy, Privacy, Accessibility) for Keyboard Maestro and Keyboard Maestro Engine off and then on again.
This especially happens if you already have Keyboard Maestro and upgrade the system. This is rather infuriating, as the checkboxes clearly show permission, so anyone would assume that means they have permission, but the system is actually lying, and you have to toggle the checkboxes off and on again to grant permission - who would even think to try that? This has remained a bug through Mojave and Catalina and now also confirmed in Big Sur.
Window positions of Alerts and Prompt For User Input windows
As described (BUG — Input Window Shifts Downward in v9.1 on Big Sur), Alerts and Prompt For User Input will move vertically each time they are opened in Big Sur. This has been reported as a bug to Apple.