Welcome back! I remember running into similar issues with the Firaxis editor no longer being able to find Civ many years ago. As you say, the game itself still runs fine in such situations.
I do not recall ever figuring out the "why" with my knowledge of that time. Though one question would be, where is Civ III installed to? Over the years of being a CivFanatic, I've seen many problems when Civ is installed to C:\Program Files, or C:\Program Files (x86), as Windows attempts to protect the files in that location (such as Civ arts, text, and scenarios), resulting in editors and related programs like Civ Assist II not being able to find the files that appear to be there. In recent years, I've always installed Civ outside of those folders - e.g. to C:\Civilization III - and have not run into any such issues. That might not be coincidental.
For Steam, the default location is most likely C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization III . You can right-click the game -> Manage -> Browse Local Files to find the location. Unfortunately, if Steam is installed to its default location, you can only move games to a location outside of Program Files if you have a second disk drive (if you have a second drive, you can add second library folder under the "Storage" tab of your account settings). Usually this is considered good as that Windows protection makes it harder for malware to modify game files, but for a game like Civ III where all its modding happens within its install folder, it's bad because it also makes it harder for legitimate humans and utilities to make modding-related changes.
As for the registry, in my case with the CD version, the key HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Infogrames Interactive\Civilization III has an "Install_Path" key set to "D:\Civilization III", which is where Civ III is installed on my multi-hard-drive desktop. I'm not entirely sure that's the right one for the Steam version though; usually I would be using that version, but my laptop is in the shop so the old desktop is the machine of the day.
One of the minor features of my editor is that if it cannot find a file, it tells you what its "last hope" for trying to find the file was. Sometimes that can provide a lightbulb moment as to what's wrong, seeing that it was barking up the wrong tree and which tree it was barking up. It may or may not run into the same problem that the Firaxis editor does for you currently, but if so, you'd have a decent hint as to where the search is going wrong, and if not, it would be functional.
