I've now compared the log from Windows 7 and Windows 10.somethingsomething. I searched for "arw" in both logs.
What stands out is that on Windows 7 the Explorer primarily uses the registry keys we're expecting; The documented ones.
For example, it looks for (and finds) the property sheet handler in HKCU\Software\Classes\arwfile\shellex\PropertySheetHandlers and HKCR\arwfile\shellex\PropertySheetHandlers.
On Windows 10 however, things are a bit different. Notably, it never looks for *arwfile\shellex\*
Both Windows 7 and Windows 10 look for (and don't find) HKCU\Software\Classes\SystemFileAssociations\.arw\shellex\PropertySheetHandlers and HKCR\SystemFileAssociations\.arw\shellex\PropertySheetHandlers.
They also read the more general keys HKCU\Software\Classes\*\shellex\PropertySheetHandlers, and HKCR\*\shellex\PropertySheetHandlers and Windows 10 additionally looks for HKCU\Software\Classes\Kind.Picture\shellex\PropertySheetHandlers and HKCR\Kind.Picture\shellex\PropertySheetHandlers.
Apparently, the SystemFileAssociations keys are related to something called Association Arrays.