Is there a flat bar style controller or shifter for Apex AXS or Apex mechanical 12-speed drivetrains?

Yes!

For Apex AXS drivetrains, use a flatbar AXS controller to shift your rear derailleur.

For Apex mechanical setups, Eagle trigger or twist shifters are compatible with both Apex mechanical and Eagle mechanical derailleurs. The S300 flat bar brakeset is available for flat bar bike builds for both Apex XPLR AXS and Apex mechanical drivetrains.