FM radio receivers were a staple of those electronic kits I used to play with as a kid. Here's what a quick Google search shows: https://www.electronicsforu.com/electronics-projects/simple-...

The difference in complexity between this and something commercial are extras like decoding the stereo subcarrier and applying the data to the main signal: https://en.wikipedia.org/wiki/FM_broadcasting#Stereo_FM

Yeah, I also did electronic kits as a kid, and both learned how to read a diagram thanks to them, but never understood what individual parts did in any circuit.

I “get” I=V/R (I mean not really… I know it exists), but how to go from there to understanding what each capacitor is doing in the simplest of fm circuits?

Is each component doing the equivalent of non-trivial real-time signal processing? How to visualize / think about it?

I’ve mentioned this on another sibling comment, but amateur radio is where you need to look. It took me about 6 months of casual study to go through all three license classes (tech took me like 2 weeks), and you learn quite a bit about everything you’ve mentioned in the process. More than that, you gain a license which allows you to legally experiment with this stuff.