Make an image plane as "environment"
When you render the Environment pass, it will use the HDRI or the conventional background images used, but if you you an "images as plane" as a background, it will be dealt as if it's a normal object.
I think you could be able to set that image plane as "environment" so that it can render separately as a pass.
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you can use multiple view layers to render your image separately, then combine it in the compositor to your liking.
Image planes are no different than any mesh object. So in order to be able to do this, you would need some form of option somewhere to force specific objects to be included in a pass they shouldn't be in.
In such case, why not just use a cryptomatte? It essentially allows you to get the exact same end result, except you don't need to set up anything beforehand, can use it on anything at anytime, and is already available?