Screen-recording Anukari has been a bit of a challenge, as OBS works best while using GPU encoding, and also seems to do things that the GPU doesn't like in general (and Anukari uses the GPU). I suspect what you're hearing in the videos has to do with that. But also I'm sure that the model for the mic compression could be improved, and I'm not sure about the default attack time, etc.
If screen recording is actually the thing causing the issue you might try CPU encoding with one of the fast lossless codecs and doing the "real" encoding in a second pass later. As a bonus, software encoding should also give a higher quality result. That does require an SSD and quite a bit of free space though.
Have you tried HDMI output from the computer running Anukari to an HDMI capture dongle on a second system, so that all of the recording overhead is offloaded?
I'm very rusty at music, but I always had a big soft spot for unusual/unique synthesis methods. I'll be buying a copy as soon as I'm back at a desktop system :).