As you can see in these images of a game the background colors are less saturated and grayer:
Do you think the designer reduced the transparency in the background or used grayer colors?
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I don't think the colours are greyer or less saturated in these examples. The backgrounds appear to be lower in contrast, but still pretty colourful. The foreground objects also have distinct outlines to separate them from the background.
Yes, most digital artists work with applications which support layers, so this is likely something done with layer opacities.
You could achieve something like the example by putting a layer filled with a solid colour between the background and foreground objects, then reduce the opacity of the filled layer to around 40% or so. Here's an example using Photoshop, but almost any software that supports layers could be used similarly.
Here's a before and after with the colour fill layer switched on and off.