That looks good!
Nothing under your home directory is owned by root.
The only things are these two links which point to files that are most probably owned by root.
discord.desktop → /opt/discord/discord.desktop
libreoffice-writer.desktop → /usr/lib/libreoffice/share/xdg/writer.desktop
I have not used Xfce for a long time so I am not aware if there are any better ways for handling this.
What I personaly would do is first remove these links.
Then I would make a libreoffice-writer.desktop and
a discord.desktop with the content corresponding to their counterparts in /usr/lib/libreoffice/share/xdg/writer.desktop resp. in /opt/discord/discord.desktop.
Not sure if this would work but that is what I personally would try.