Put your BW noise image into a layer mask of an adjustment layer or an image layer.
Here it makes the solid blue color layer partially visible:
And here it allows the Hue&Saturation layer to cause hue shift to red:
The idea is used here How is this type of grain/noise effect made? to allow noise to make a photo grainy so that the graininess is darkness:
You can get layer mask onto the screen for pasting and other easy to see edits by clicking the layer mask icon in the layers panel and holding Alt at the same time.
Often it's useful to apply Image > Adjustments > Curves to the layer mask to make it more effecive. With layer opacity you can only make the layer less apparent.
With blending modes you can get weird effects:
Not asked: The weirdness has no limits if you filter or edit otherwise the layer mask. You can keep the image visible all the time to see what you got, only click the layer mask icon without Alt to get the mask under editing.
Layer masks are BW images, but having RGB mode doesn't harm at all, it works anyway. Photoshop desaturates the mask.