This is very embarrassing, but I found a solution after some brief experiments.
Apparently, the first entry of the Path variable should NOT contain %appdata% or %localappdata%. It MAY contain %userprofile%.
For example, the first entry before Windows recognizing it as part of Path was:
%appdata%\Python\Python36\Scripts;
Windows started to show the Path editor correctly after I modified it to:
%userprofile%\Python\Python36\Scripts;
Probably has something to do with evaluation order. Or maybe just oversight.
My other machine worked because it had "%USERPROFILE%\AppData\Local\Microsoft\WindowsApps" as the first entry.