When I right click on an image in the develop module there is no Edit in... option on the menu
I have checked that the registry key HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\
as described in various searches and it is present and correct
The preference file can get corrupted, resulting in odd behavior. Some people have a knee jerk reaction in thinking they need to uninstall then reinstall Lightroom Classic, maybe that could be called for, but it would be better to first reset the preference file.
Unless you used Adobe Creative Cloud Cleaner to completely remove the programs, the existing preferences file may have not been deleated during uninstall, and not replaced during install.
Be aware that resetting the preference file will result in Lightroom Classic creating a new catalog instead if opening your previously opened catalog (normally) so make sure you know where your catalog is.
Be aware the resetting the preference file will revert some settings in Preferences to defaults. So be aware of what you have changed, so that you can put those back the way you want them.