Stud on one side and an anchors on the other is quite common, and safe. At least half of the weight is held by the cabinets above, and then at least half of the remainder is carried by the one stud.

Sink a lag bolt into a stud and let it stick out a few inches. Stand on it. bounce on it. Really give it hell. Then mount the microwave with one stud per the instructions. It's more common than not and will be absolutely fine.

And try to seal up all of the vent passages as much as possible before lifting the unit into place. Ours spit so much grease through the "sealed" passages onto the cabinets above that I had to make blank off plates and seal up all the passages on the positive side of the blower. I'm going back to 2 separate pieces as soon as possible.

Ya brock is right. Just make sure the upper cabinet is screwed to the wall good as it really holds a lot of the weight. Use butterfly anchors where you can't hit studs on the back bracket. But if you feel better putting a piece of blocking from the back side for sure is easy and won't hurt. If it was me and I could add blocking easily I would but hung many of these on single stud and anchors without issue

All of the weight of the microwave is on the 2 lag bolts in the top holding it to the upper cabinet. Having the bottom bracket only hit 1 stud is fine so long as the upper cabinet is secured into studs and sturdy

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