JACK isn't very complicated at all if you use something like Cadence.
You don't have to build anything 'from scratch'. Cadence has a nice interface that makes using JACK very simple, it is no more complicated than VoiceMeeter. I would even argue that VoiceMeeters UI is more complicated, which is more true for VoiceMeeter Potato than the basic version.
JACK is much more powerful than VoiceMeeter thanks to the Catia patchbay in the case of Cadence. You can route your audio with no restrictions, so there is no need for seperate, more advanced versions of the software, and usually applications route themselves automatically. You just connect the nodes to route your audio anywhere you want. It's also lower latency.
Lots of programs support JACK, but not all, so I would recommend enabling Pulseaudio bridge and ALSA bridge so programs go through those and end up in JACK, so you can still route them. More on that and a basic setup guide here.
If you need some more control over the routing like adjustable volume sliders, you can try pairing Cadence with PatchMatrix, but that will feel more like making your own mixer, which isn't a bad thing inherently.
You say that you don't want to build your own mixer because you probably fear that you will get overwhelmed by the options or that it would take too much time, but that's just not true. Just adjust and add anything that you need and ignore the rest, it won't get overwhelming when it doesn't need to.
It also helps with clutter and bloat, for example VoiceMeeter Potato has a few effects built in, but I found no practical use for them, so they became unnessecary buttons cluttering up the mixer. You mostly get only the basics and if you need anything extra, you download it separately.
Cadence and it's tools are available on the Community repo here. I really recommend you give it a try. It makes setting up JACK very simple and it's just so much better than VoiceMeeter that I don't miss it a single bit.
As for Zoom, you will just have to wait for them to reply or it could be that the Linux client just doesn't have any audio processing.