There are no gravitational waves from Jupiter. The sources that you describe are popular science, which is science that is misinterpreted and oversimplified.

The theory states that there are only gravitational waves when there is a huge loss in potential energy. This causes objects to circle towards each other. This circling has never been observed directly. Instead we see the moon circle away from earth, and earth circle away from the sun. That is In the opposite direction.

What is observed is a time-delay, which might be related to the time-slowing effect of gravity. It does not proof any "speed" of gravity.

In essence the theory around the speed of gravity is a bit circular.
It first assumes that it moves with the speed of light, and uses the special relativity corrections. This means that the force is corrected for the linear movement.
Then it also assumes that it bends space-time and this gives us the general relativity theory.
There is no direct proof of gravity going with the speed of light. But by providing evidence for the general relativity theory scientists assume that it is.