I've been trying to figure out how to make IIR filters for a software modular synth, off and on for years now. (Basically, given parameters like cutoff frequency and dB per octave rolloff, how do I find the filter coefficients? There must be closed-form functions for this buried inside VCV Rack, Audacity, and LMMS somewhere, but the code is hard to follow. I don't know how all the Wikipedia articles and DSP guides manage to skip over this step, the only step I don't understand. Some of them even punt to "Call this Matlab function" or "Use this PHP page that generates C code for you" Bleh!)
I did encounter this book, but it still couldn't help me figure it out. I bookmarked it to try again.
First: cutoff, resonance, filter slope, etc., can be built with FIR (finite impulse response) filters. You can describe the passive circuit with a transfer function, which can be implemented in DSP using a z-transform. You can also describe a filter with poles and zeroes, and transform those. There's a bunch of resources on the web, e.g. https://ccrma.stanford.edu/~jos/filters/, but many assume you know something of electronics.
Recurrent filters don't have closed form solutions, and their implementation is a bit of an art. Plugin maker Urs Heckmann (from u-he.com) did a (rather successful) attempt at modeling the filter from an old synth with various implementations, and let people test them in the wild. He blogged about it, but I can't find all relevant posts. This might be a starting point: https://urs.silvrback.com/zero-delay-feedback
This course (https://www.staff.ncl.ac.uk/oliver.hinton/eee305/) is based on a book and links to the chapters, but there's a lot more (check the websites of MIT or Stanford's EE department for online courses).
They are the classic IIR biquads. If you want steeper filters, just run multiple equal filters in series (high-order IIRs are prone to numeric instability).
I've had similar struggles. I found this comparison between Ableton's EQ Eight and Pro-Q by Dan Worrall [1] to be incredibly (and unexpectedly) informative on the subject. He is a very good teacher and an expert in the area. Maybe it might on your journey.
I did encounter this book, but it still couldn't help me figure it out. I bookmarked it to try again.