Colour fill effect

I want to create a scene that begins with all objects 'grey'. The scene is a low poly animation with characters and objects etc. so the characters will be moving as the following effect is happening.

The effect I want to create is that the scene is 'filled' with colour. So, from a specific location in the scene and it grows. I know I could set up a mix shader and keyframe this (for each mesh). Is there a better way to achieve this? In my mind, I am thinking of a second object, e.g. a cylinder that scales. The cylinder is not visible, but everything inside the cylinder is seen in the correct colour, whereas outside is grey.

To make this even better, as the colour 'grows' across the floor, colour would then grow 'up' objects such as furniture and characters. Could I achieve this by having multiple 'control' objects? Or is it easier to use a sphere or even an empty and somehow use the distance to the empty? Am I even on the right lines or going down a rabbit hole!!

I can't find anything on this effect in the usual places, but it could also be my poor use of search terms! I hope the description is good enough. Hope you can point me in the right direction.