For the sake of simplicity, the focus here will be on gifs that are almost stationary.
1. Have your sharpened and coloured gif ready.
2. Make a new layer and rename it blur.
3. Select the blur tool. I’m going to change the brush colour to black and use the soft round brush. Set the strength to 50% and check the box for Sample All Layers.
4. I paint over the noisy areas like the walls. If the effect isn’t strong enough, you can increase the percentage of the blur strength. Or if the blurring makes your gif look too unnatural, you can lower the opacity of the blur layer.
I kept the noise on the stairs for texture.
If you need further clarification, feel free to send me an ask.