Recently, I switched from Notepad++ x86 to x64 on my computer at work. There the admin account differs from my user account.
With the x64 version, my own user doesn't see the "Edit with Notepad++" menu item in the modern explorer context menu. It is available in the old explorer:

If I login with the admin account, I see the modern menu item, but not the old menu item:

Here is the installation log of the x64 install:
notepad_x64_install.txt
On my personal computer my user is also admin, and here the context menu item is available. So it seems to happen only if the admin account is a different one. In 2023 I reported a similar problem for the x86 version: notepad-plus-plus/notepad-plus-plus#13476
At first try, I think I simply started the x64 installer which asked to remove x86 version (not sure about this, maybe I uninstalled x86 first) - here the old menu item was not properly removed and remained in the the context menu, but without icon and of course non functioning. I fixed it by
- uninstall x64, reboot
- install x86, reboot
- uninstall x86, reboot
- install x64, reboot