This question made me think. Since sometimes I also want to do this, but the UI doesn’t let me. But the filtering also goes into the URL. And I just succesfully hacked a working deep filter into my URL.
If you filter something, you see the URL change to something like:
&filters[$and][0][contentTheme][$eq]=dark
if you change this to something nested, it works. In my example
&filters[$and][0][background][color][$eq]=grey