why isolate the run capacitor from circuit when off?
You are correct. For a reversible PSC motor that has two identical windings, the simplest way to reverse the motor is to connect the capacitor between the two windings and use a SPDT switch to select direction. A better scheme than that is to use a SPDT switch with a center off position so that the same switch can be used to start and stop the motor. The previous question was specifically about the possible wiring configurations using a DPDT relay. The diagram was intended to show how the mis-wired relay might have been intended to be connected.

The configuration described in the second part of the question may be intended to force a delay between forward and reverse operation. It could also be something done to accommodate a means of overload protection. There are a lot of single-phase motor configurations. A diagram of a specific configuration is needed to explain it.