Vine a threat?
This is a type of native grape vine.
It has wildlife value for songbirds, reptiles and small mammals.
It won't smother trees to death like other invasive vines, but you are correct, it will compete for sunlight with your broadleaved shrubs and could cause areas to dieback.
You can remove it if you like by digging it out.
You will have to check if allowed in your area, but you could cut the vine down low and immediately 'paint' (a sponge brush works well) just the cut surface with an herbicide containing the active ingredient glyphosate. There would be little chance of runoff from that method.