Is the ".." in the path a mis-type?
I know that we tend to vocalize /usr as "user", but is "/user" also a mis-type and should the path be
/usr/share/applications/org.gnome.Brave.desktop
I can understand the urge to "tweak" the panel via the stored configuration (text) file, but wouldn't it be simpler to just "drag+drop" the icon from the system menu onto the Panel, then do those tweaks on the resulting file?
Just make sure that before making changes to the Panel layout, you right-click on the icons that need to move, and "uncheck" the "Lock to panel" option. That will make those free to be dragged around for a new placement and allow auto-adjust if you want to drop a new icon between the other two that you mentioned.
To make sure there is no doubt as to which of the files under
/usr/share/mate-panel/layouts
that you then need to tweak, I strongly recommend you save the new configuration as a "Named Layout" using MATE Tweak.
To do that, follow the guidance provided in the bottom half of the this posting.
If you go straight to text editing of the *.layout file, I think you may need to either reboot or restart the systemd service that manages the Panel interraction to force it to reload your modified *.layout file.
IMPORTANT: When I saved my custom Panel layout, the system saved two files with the same "custom-named" basename, but one file with each of the suffixes as follows:
-rw-rw-r-- 1 root root 4266 Mar 21 2021 Oasis_DEFAULT-tweak.layout
-rw-rw-r-- 1 root root 3942 Mar 21 2021 Oasis_DEFAULT-tweak.panel
There is this other discussion, which does involve the dual-file custom panel setup. It may offer you some other insights.
This other discussion gets into a number of aspects and "gotchas" relating to Panel customization. It also may offer some other insights.