I use tofi. Dmenu_extended doesn't appear to be packaged in Debian, and I can't claim experience with it.

Most programs will do what xdg-open does. I also don't see anything in a ten second glance at dmenu_extended's settings for creating file-file-to-program mappings. So I'd probably try xdg-open on the file first to confirm that it's truly behavior specific to dmenu_extended.

If it is just dmenu_extended:

https://github.com/MarkHedleyJones/dmenu-extended

Menu configuration is contained in a JSON formatted file found at ~/.config/dmenu-extended/config/dmenuExtended_preferences.txt that controls the appearance and functionality of the menu. This file is also accessible from the -> Menu configuration submenu as * Edit menu preferences

I'd probably take a skim through that.

And other problem that I’m facing is that when I try to open Steam (installed as a flatpak) it never opens, instead gives me this error message:

xdg-open: file ‘/usr/bin/flatpak run --branch=stable --arch=x86_64 --command=/app/bin/steam --file-forwarding com.valvesoftware.Steam @@u’ does not exist

I don't know what you mean "try to open". Using dmenu_extended? Using some other program to launch it?

So, xdg-open is gonna look at ~/.local/share/applications/*.desktop files to determine what command to run.

I don't use that whole system of XDG file-program associations or flatpak, so I've got limited familiarity with them.

But the basic problem you're facing is that you want the right command to be invoked. I'd try and get flatpak Steam launching from the terminal first. Once that's okay, then go looking at those .desktop files.

Gosh, if it weren't for the --dmenu argument for rofi, I'd have forgotten dmenu still existed. Do people still use dmenu?

Out of curiosity, why do you chose dmenu over rofi (or, I think it's wofi for Wayland)?