@re-touch, this is interesting. Some brief replies:
-- IRL, a full rectifier should give the absolute value function you're speaking of (unless I'm misunderstanding)
-- do you use VCV rack? (https://vcvrack.com/Host) That would give you another (and deeper than Softube) software platform to play in and test the above hypothesis, though it is still software
-- while I'm still pretty new to hardware modular, I find my "more unique" filters REALLY surprise me if I go beyond "routine" settings. So the response per the settings you mention above MAY vary meaningfully depending on the filter unit.
That said, a more experienced modular user or electrical engineer could maybe give you a definitive answer. Maybe baseline unit noise, with feedback, gained into overdrive (with gain varying the spectrum or "color" or results) would produce similar results across filter types.
Cheers!
NG