Why doesn't a microwave heat the air around food, in addition to the food itself?

Buy an oven which combines a grill and microwave or even a full oven and microwave.

But remember that when you use the grill or oven settings you need containers that can take the heat while if you use the microwave settings you need containers that do not have metal.

So if you combine microwave and traditional over heat, you need a container that neither has metal nor will melt.

Or first use one setting, than move your meat to an other container and use the other setting.

In the microwave setting, the air will warm up a bit, as does the container, but not enough to brown the meat. That is how microwave ovens work, they heat the 'water' in the food, so will easily get it to boiling heat, but they do not heat the outside of the food.

Every material (air, water, metal, plastic...) are more or less conductive and proportionally more or less absorbent of radiowave.

The more it absorbs the less material it needs to absorb a significant amount (let say 90%) of the wave energy.

For a given frequency and a given material you can calculate the amount of material you need to catch a given quantity of energy (heat).

This is a consequence of the skin effect.

For water the skin depth is about 4cm for microwaves and air is several meters, like km.

In other words, 90% of the microwave energy is absorbed by 4cm of anything with water in it, e.g., food.

Microwaves are actually lower energy photons than even visible light. So they don't cook because they carry high amounts of energy per photon, to impart to whatever they touch.

They cook for one reason only: they might be lower energy, but water and some other food molecules are electric dipoles (meaning their structure puts distinct positive and negative charges separated at different places in the molecule) and therefore they will rapidly rotate as they try to align themselves with electromagnetic waves across several ranges of microwave frequencies (even though these are not ionising radiations). Microwaves used in ovens typically have frequencies between 900 million and 2.5 billion Hz (cycles per second). That rotation in effect transfers energy to the molecule and its nearby molecules as heat. So a passing microwave of the right frequency can easily transfer its energy to a water molecule, and cause it to rotate quickly or jostle nearby molecules - which translates as being hotter. It can't easily transfer its energy to nitrogen or oxygen molecules in the air, most plastic/ceramic/glass used for food containers, and so on.

And that's what a microwave oven does. It sends a torrent of low energy photons into the cavity, they bounce around, and when they interact with molecules (and their energy is transferred), its very likely to be water, fat and some other molecules which mainly exist in the food. They don't get absorbed by the air, so the air itself isn't heated up. (A bit like how air isn't hot due to visible light travelling through it.)

Apart from perhaps some specialist materials engineered for the purpose, and some low-level absorption, any significant heating of containers, air, etc, only happen because of energy transferred to water in the food, which then warms the air and containers in turn., or evaporates as steam.