I’m testing the Pi HQ camera with a C-Mount Tamron lens that gives similar bokeh for a total cost of around $100... but it is awkward and a little clumsy, and offers no autofocus, so you have to be careful to not move out of the prefocused area.

So in other words, it’s easier to just use a good mirrorless camera.

I have a similar setup to OP, but I bought a used Sony a6000 and the same lens on sale, so the camera and lens only cost me about $500. You could use the Sony kit lens too, and it would still be a huge upgrade over any webcam.

Any camera with an f/2ish lens will do it, even $150 ones (but it also depends on the size of the sensor). You might not be able to use it as a Webcam directly, though.

I'm using my phone, there's an app that lets you stream from your phone's camera... which is usually better than the dedicated web cams.