Why does adding salt to microwaved broth make it foamy?

There are likely two or three things happening.

When clear liquids come out of a microwave, it is quite common for it to froth as soon as you put something into it. A spoon, or crystals of salt or sugar forms nucleation sites for over-energised water molecules to make vapour bubbles. Water forms vapour at any temperature, not just at its boiling point.

In conventional heating, convection starts from the layer closest to the heated bottom of the pan and the hottest liquid always rises to the surface and there is plenty of movements in the liquid body. In a microwave energy goes into the water molecules directly and the container is heated by the energiesed liquid, the opposite of conventional heating. There is very little time for convection currents to develop. Molecules within the body of the liquid that are excited may not find sites to form vapour and become locally superheated. Vapour pressure above the liquid may be actually less than what it should be at that temperature until the body is disturbed. Lots of tiny vapour bubbles are released when disturbed. They look foamy until they escape from the liquid. This is the most likely cause.

Salting out of proteins could be another cause, though probably less likely. You would probably see a layer of scum on the surface that would not disappear.

Emulsion breaking. Heating and addition of salt will encourage any emulsion to split. From your picture, there is plenty of oil around. There could have been some oil droplets suspended in the water phase of the soup. These could clump together at the start of emulsion breaking giving a cloudy appearance before floating to the top as a continuous layer. Not likely either.