Is it good Feng Shui for a rural double-detached house facing north and south to have a recessed bathroom on both sides of the backyard and then surround it with a wall?

This depends on the degree of concavity. It is difficult to judge just by talking about a concave. Generally speaking, the backyard is a basalt for a Yangzhai. It is better to be thick and concave is taboo. It depends on the size of the situation to decide whether it is appropriate to fill it with soil. It is best not to build the toilet directly behind it. It depends on how both sides decide. However, no matter which side you choose, there is always something ominous.

Fences, you can have this.