When I export png from Character Animator it looks much more crisp at 100%. But still I can't zoom in on the figure as has exported at 1920x1080.
Not sure if an answer, but what I do is export videos from Ch as much as possible, so it renders at the right size. I also went through and set any resolution settings (e.g. Illustrator has some settings somewhere - Document Properties I think) as high as possible. Not sure this matters, but I then copied each file across.
I suspect the most important thing is to not export PNG images and then resize them significantly in AE. Instead, I think if you use "dynamic linking" then AE will ask the CH libraries to render at the resolution it wants them at. On my little laptop this is pretty slow, so I minimize the number of scenes I do it for (but I do use this for some scenes). It comes out fine for me then. E.g. drag the puppet from the CH window directly into the AE project panel, which creates a dynamic link. If you update in CH, AE will pick up the changes.
But most of the time I personally now render videos per scene from CH as much as possible doing all the scaling there. E.g. to put a cartoon over the top of a video file, I will render using "QuickTime/GoPro Cineform 12bit RGB with alpha" - the "with alpha" meaning the video preserves transparency. Then I use AE to superimpose that video over my background video rendered by something else (Unity 3D generated video in my case).
I frequently now do full body shots or zoomed in shots of the face from the same puppet, with no fuzziness.
Oh, I am using 6000x6000pt Adobe Illustrator files in case that makes a difference. Also in Illustrator if I go to "File / Document Setup", I pick the "High Resolution" drop down preset. I don't know if it makes a difference (once I got it working, I stopped fiddling) - just saying what my file is in case useful. In CH I don't use render as vectors as I want gradients to work - so CH is rendering as bitmaps - but I make sure what it outputs is the right final resolution (not a full body shot PNG that I then zoom in AE).