Changing the power supply depends on the requisite voltage and current draw the new lights need. If there is nothing wrong with the wire and the anticipated current draw does not exceed the existing system, there is no need to replace it.

Otherwise, you'd need to use a wiring gauge calculator to figure things out.

The transformer is capable of lighting 600 watts, maximum. That doesn't mean it's pushing 600 watts. The transformer only pushes what's required by the lights, or in your case, 22 watts.