Assembly theory approaches the question from a different angle but largely reinforces this conclusion. Essentially, anything past a significant level of chemical complexity is a sign of life. DNA is astronomically unlikely to form spontaneously. It was designed by co-evolution. If you find a screwdriver on an alien planet, you can deduce the existence of screws, machines that require fasteners, and ultimately a living being that built those machines.
In the history of the universe, we only know of a single instance where something ejected from planetary atmosphere by its own force. Humans, when we launched a rocket into space. That's it. Debris enters planets atmosphere but we never see a rock LEAVING an alien planet on its own power. Except on earth.
A planetary system with evidence of panspermia would be a similar phenomenon to DNA, a screwdriver, or a rocket - clear evidence that life was at work to produce something otherwise so implausible.
This works so well as a framework for finding alien life since it makes no assumptions about what life is or what it consists of. Only that it produces complexity.