Microwave installation - venting
I hate venting through the back, can be done.
As you see, typically the piece in the first pic is to be installed before hanging the microwave. This almost makes it impossible without cutting a huge hole behind the oven first, Just so when you swing the oven up into place the piece will clear.
This will be covered by the back of the oven, but no way to repair the drywall.
In one new home, had the hvac guys install the duct work during rough in.
Only need to be 1/4" off on rough in and is a problem.
Anytime I exhausted out the back, even though it is an option, has always ended in a compromised situation.
If possible, I would suggest going through the top of the cabinet, then 90 out to the garage and 90 up.
More 90's you add the more restriction you get in air flow.
Assuming have drywall in the garage, you could cut a larger hole then needed for room to work, mark and locate the hole for oven and cut it out from the garage side, get the duct through the wall, then patch the larger hole in the garage.
Would like to hand you a easy button, I do not see it in this case.
If it was easy, we would not call it work!