The Kbin code is AGPL, so that will likely become the license for the actual art assets if it's put in place officially. The current folder logo is already in the repo and under AGPL. If I were Ernest and wanted this to be part of the project I would ask you to submit it as a PR to Codeberg (and sign any necessary CLAs) so that the assets are properly placed into the repository under its license.
For now you can use CC-BY-NC-SA like you suggested which would allow for profile pics, magazine sidebar images, fan art, and the like. Since this is a SA license the users and mods need to have their modified images released under the same license as well. For a PFP attribution and indication of the license would be difficult and most people probably won't care. Also note that the CC license is irrevocable and people are allowed to use the assets freely outside of Kbin as long as the terms are followed.
As a 3PA dev or a Kbin instance owner I would not touch anything with NC as there is some ambiguity in the NC clause which might be trouble for an instance which say is not for-profit but accepts donations. In addition if the app was open-source they would need to separately license the artwork to maintain compliance with CC-BY-NC-SA.
In the future though Ernest might want to trademark the mascot along with the name Kbin so that it will be used exclusively to represent the project. This would probably require a formal release from you (AGPL won't cut it here) basically giving them the rights to to do whatever they want with it.
Yeah this stuff is messy :) but it's good to know about it and get the conversation started now. I'm actually about to get this account deleted but thought it was worth mentioning this as I've been following the Kbin mascot ideas from the start.
BY-SA is officially listed as one way compatible with the GPL (basically you can distribute a BY-SA asset under the GPL), with the detailed analysis shown here. Kbin is under the AGPL which to my knowledge is not listed as compatible, but it should be fine as AGPL is basically GPL with the condition that the source must be released if the modified program is run on a server and not directly distributed. Keep in mind that BY-SA does allow commercial use and basically is the art equivalent of software's GPL.
IMO the cleanest way to do this would be to distribute Kibby under AGPL directly to Codeberg or grant rights under a custom agreement if Ernest wants this to be the official mascot. Alternatively the Kibby asset could be released under a second license and people hosting their own Kbin instances would have to comply with the second license to use the mascot. This could work as Kibby isn't required for Kbin to function instance owner could easily substitute a different image if they don't agree with the license.