Well - how handy are you?
I detest the recirculation vent method. That's what mine had, but no more.
The rear red wall at the ceiling, where does that go? Second floor or attic above? Sounds like it backs to a bedroom. What is below - crawl space, slab, basement?
Use the wall as a chase and run 3x5x12 duct in the wall. You will either go up the wall or down below depending on what options you have.
Open the wall up at the center of the cabinet. Put in a 3.5x12 duct. If going upward, cap the bottom of the duct about at the bottom of the cabinet while continuing up the wall. If going downward, cap the duct about at the top of the cabinet opening. Once the duct exits the wall, say into attic or joist bay, you can transition to 6" round and then to your wall cap or roof cap. Seal all seams with mastic or proper foil tape.
Most microwaves can be set to recirculate or vent by removing a plate, sometimes flipping the fan motor around. Get your manual on-line via the model number. Then cut a rectangular opening thru the wall aligning with the exhaust port and to the duct. I line the perimeter of the opening with weatherstrip that has 2-sided tape. Install microwave and enjoy.