"Program Files (x86)"is notionally where 32 bit apps live, one of the changes in version 6 was that the 32 bit version was scrapped.
Multiple versions of calibre can be installed on Windows - do a search for calibre.exe on all your drives, if 5.39 is executing it must be there somewhere.
And check the properties your desktop, taskbar, and start menu shortcuts - should look like this:
Is the FT button in the search bar?
BR