configManager.current doesn’t work then you must have been putting it into the wrong console (there are various types in Firefox that you get to from different menu items and shortcuts so it’s easy to end up with the wrong one for the particular debugging task you’re attempting).
configManager.current.siteConfig may be missing if there is no site-specific configuration (although perhaps only when there has never been any configuration - I can’t recall the details of that now).
It sounds like the site-specific settings part of this might be a red herring, although it is strange that you say in your first post that this problem with the Kee logo not appearing in the form field is only since you experimented with site-specific settings.
It would be worth checking if you modified the whitelist and blacklist settings that apply to all sites - if the form was previously being whitelisted and now is not, or is now being blacklisted, that would explain the problem.
There are some fixes in version 2.4 that could potentially relate to this problem too. You can switch to the beta version to test the changes now by installing the signed beta XPI from https://github.com/kee-org/browser-addon/releases/latest
Otherwise, v2.4 is likely to be pushed out to all users in the next week or two.