Duplicate icons on Application Menu

[github2099]

First of all, the issue not related to RedNotebook, I just happen to use it as an example.
I tested the same procedures on Fedora, Linux Mint and Pop!_OS (gnome cosmic)

1. installed the application as flatpak. and I created a new .desktop and saved in ~/.local/share/application
   It is expected to override the one comes with the flatpak installation.
   (Cosmic alpha 6, with kernel 6.12.10)

2. Searched with Launcher, it displayed the application correctly, with the revised name.

3. When using the application menu, however, it displayed two icons of the same application (from original .desktop and new .desktop)