Turn signals don’t work when headlights are on

It doesn't "act as a ground." That is your park/ tail power jumpering over to both lamps. That is poorly drawn. The diagram might lead you to believe those wires join at the lamps. In fact each wire to each lamp goes to a different filament, one goes to park, one goes to turn. The ground is the little "dashed arrow" sign pointing down from the lamp

In this case the aftermarket diagram from MyMopar is actually drawn with more detail and accuracy

View attachment 1715540068

If you look where I left my "mouse" when I took the shot, this terminal is the jumper wire for the park circuit that interconnects the left and right park filaments. Also, this is drawn more like what the lamp SHOULD look like in schematic form. You have two filaments with a common ground.........two lamps in one
Next chance i get I will try to ground out the bulb socket outer case to see what if anything changes.