As others have mentioned, dithering doesn't really play well with compression; it adds lots of fine detail noise, while lossy compression tends to smooth things out. Also modern compression like AVIF doesn't understand palette color formats (iirc avif generally uses yuv), so that kinda loses the only thing that dithering has.

I've tried it out, I'm still getting smaller AVIF files with dithering. Not like the saving you get by using a dithered png instead of a jpeg.

Depends on a lot of factors. You can keep turning the quality down on avif and get it lower than a dithered image. At some point I'd prefer the crispness of a dithered image over a blurry full color image.

Also, avif seems to do a really good job of lossy compression on dithered images.