I. AM. TRULY. BEAT!!!
I booted into High Sierra, changed my search engine pref time after time after time, and searched with Find Any File after each change, and not a single search, either by name, file content, or last modified date identified whatever changed along with my pref.
¯\_(ツ)_/¯Update: Found it!
Well, maybe.
The only file in High Sierra that changes as I change my search engine pref is /Users/artie/Library/Preferences/.GlobalPreferences.plist. Note the dot. I originally missed the file because I was filtering out invisibles.
<key>NSPreferredWebServices</key>
<dict>
<key>NSWebServicesProviderWebSearch</key>
<dict>
<key>NSDefaultDisplayName</key>
<string>DuckDuckGo</string>
<key>NSProviderIdentifier</key>
<string>com.duckduckgo</string>
</dict>
</dict>
I'm confused, though, by the info being stored in two places in Catalina, i.e. the file I previously identified AND this new one.
The file in question seems to be the repository for an awful lot of prefs, so I hesitate to tell Rain to delete it.
I've got no idea where to go from here.