Hi Kehel18! Thanks for your reply! I actually looked into using custom depth but I ran into the problem that the stencil is exactly around the object, where for my needs I preferred something that would extend beyond it and blur into the background a bit.
In the end I managed by just putting a sphere over the object and applying the same mosaic blur from my original material graph that I posted to the sphere, using the SceneColor to set its emmisive channel. Then I faded out the sphere material by applying a fresnel node to its opacity channel.
Technically, I think it should also be possible to use the fresnel node to blur the alpha mask for the post-processing material in case you are using custom depth after all. This would be a more effective and generalizable approach, but tbh I can’t be bothered anymore and what I’ve got now looks good!
Thanks again, I’ll mark this topic as solved 