Could posts and beams in this design be modified with tenons and mortices and then exported via STL to a multi-axis CNC machine ?
Sure. An STL is an STL. Your CAM processor is the bridge to your CNC.
I was lead Sawyer in a Glue Lam plant when I first moved to Oregon. I used to cut Glue Lams to spec up to 110ft long, over 10,000 board ft. each. Specialized in repairing them. My biggest saw, a 2 story band saw. Fun stuff until it’s time to change the blade. Often we’d cut kits like this house.