Spouse Sponsored KITAS

IMHO and according to my agent even on a Kitas if your wife owns a business you can slightly give a hand without being troubled BUT she has to be there at all times you will give that help.

Also notice that with a Family Kitas already in your hands you can be hired by a company and it will only need to process IMTA, which makes the whole process much quicker and easier

The OP is about right.
A legal marriage to an Indonesian pretty much guarantees a KITAS with an extremely likely trouble free KITAP after two years but these don't allow work as such.
A wife sponsored KITAS holder isn't supposed to work at all but that seems to be largely ignored as long as the work is informal, part time or things like school visits, and you keep your head down.
Wife sponsored KITAP holders get a lot more flexibility so can get away with working longer hours and more openly. The law is clear, a KITAP holder can work in order to look after his family but the work department bods say that's fine only if you have a work permit.
The safe way is working online, a family business, or some other part time stuff that brings in enough to live reasonably.
I suppose it depends on your skill set as to what you can do to earn your bread.

It wasn't always easy but I did that for 10 years and managed fine once I'd got the hang of how to earn without breaking any laws that anyone cared about (It's possible I bent a few)