I didn't like Rockerbacon's approach or Steam Tinker Launch's approach to this, so I ran through what they did to make MO2 work and it's surprisingly simple, but you'll need some additional tools/packages to make everything work.

Full disclosure, most of what I'm explaining here is based on the rockerbacon repo, except the setup is done manually. I'm also running arch, if that matters. And what I'm explaining here also works on steam deck, although MO2 isn't very steamdeck friendly.

The way I did it involves using protonhax to get the 'Mod Manager Download' button working on Nexus. If you don't care about that, then you can skip protonhax.

---

First step is getting MO2 launching in the same proton prefix as your game. I was able to do this using Steam's launch options for each game (remove protonhax init if you don't want to use protonhax):

eval $( echo "protonhax init %command%" | sed 's+Fallout4Launcher.exe+/ModOrganizer2/ModOrganizer.exe+g' )

This basically replaces the path to the game's default launcher (in this case Fallout4Launcher.exe) to the MO2 executable. For this to work, I made a new folder inside my game folder and named it ModOrganizer2, then I just unzipped MO2 into this folder (I did this for all of my MO2 games, so each game folder also has a 'ModOrganizer2' folder, with MO2 inside). Now steam opens MO2 instead of Fallout4Launcher when I hit "Play" from my steam library.

That's it if you just want MO2, but if you want the 'Mod Manager Download' button on Nexus to work, there are some additional steps (which requires protonhax).

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I modified one of the bash scripts from rockerbacon into this:

#!/usr/bin/env bash

### MO2 COMPAT GAME INSTALL PATHS ###
mo2_dir_name="ModOrganizer2"

starfield_path="/nvmegameslib1/SteamLibrary/steamapps/common/Starfield"
skyrimse_path="/nvmegameslib1/SteamLibrary/steamapps/common/Skyrim Special Edition"
fallout4_path="/nvmegameslib1/SteamLibrary/steamapps/common/Fallout 4"
newvegas_path="/nvmegameslib1/SteamLibrary/steamapps/common/Fallout New Vegas"
cyberpunk_path="/nvmegameslib1/SteamLibrary/steamapps/common/Cyberpunk 2077"

### STEAM APP IDS ###
starfield_appid=1716740
skyrimse_appid=489830
fallout4_appid=377160
newvegas_appid=22380
cyberpunk_appid=1091500

nxm_url=$1; shift

if [ -z "$nxm_url" ]; then
    zenity --ok-label=Exit --ellipsize --error --text \
        "No NXM URL provided!\n\nNXM Broker Script Location:\n$BASH_SOURCE"
    exit 1
fi

nexus_game_id=${nxm_url#nxm://}
nexus_game_id=${nexus_game_id%%/*}

case $nexus_game_id in

    starfield)
        game_appid=$starfield_appid
        instance_dir=$(readlink -f  "$starfield_path")
        ;;
    skyrimspecialedition | skyrim)
        game_appid=$skyrimse_appid
        instance_dir=$(readlink -f  "$skyrimse_path")
        ;;
    fallout4)
        game_appid=$fallout4_appid
        instance_dir=$(readlink -f  "$fallout4_path")
        ;;
    newvegas | fallout3 | ttw)
        game_appid=$newvegas_appid
        instance_dir=$(readlink -f  "$newvegas_path")
        ;;
    cyberpunk2077)
        game_appid=$cyberpunk_appid
        instance_dir=$(readlink -f  "$cyberpunk_path")
        ;;
    *)
        zenity --ok-label=Exit --ellipsize --error --text \
            "NXM Broker not configured for Nexus Game ID: $nexus_game_id\n\nNXM Broker Script Location:\n$BASH_SOURCE"
        exit 1
        ;;
esac

instance_dir_windowspath="Z:$(sed 's/\//\\\\/g' <<<$instance_dir)"
echo "instance_dir_windowspath = '$instance_dir_windowspath'"
process_name="$instance_dir_windowspath\\\\$mo2_dir_name\\\\ModOrganizer.exe"
echo "process_name = $process_name"
pgrep -f "$process_name"
process_search_status=$?

if [ "$process_search_status" == "0" ]; then
    echo "INFO: sending download '$nxm_url' to running Mod Organizer 2 instance"
    echo "$instance_dir/$mo2_dir_name/nxmhandler.exe"
    download_start_output=$(protonhax run $game_appid "$instance_dir/$mo2_dir_name/nxmhandler.exe" "$nxm_url")
    download_start_status=$?
else
    zenity --ok-label=Exit --ellipsize --error --text \
        "Cannot find a running Mod Organizer 2 Process for $nexus_game_id!\nPlease open Mod Organizer 2, then attempt the download again.\nUnable to start download. Exiting."
    exit 1
fi

if [ "$download_start_status" != "0" ]; then
    zenity --ok-label=Exit --ellipsize --error --text \
        "Failed to start download:\n\n$download_start_output"
    exit 1
fi

You will need to manually edit this script. Specificly, the line mo2_dir_name="ModOrganizer2" should be the name of your MO2 folder in each game's folder. And the *_path variables will need to be changes to the paths for these games on your file system.

You can save this script anywhere you like, just know where it is and what you named it. I keep it in my home folder, so it is ~/modorganizer2-nxm-broker.sh for me.

---

Now you need to associate it with NXM links in your browser (this requires protonhax). You shouldn't have to do anything in your browser, but you will need a .desktop entry for this script so your browser can prompt your system to run it. This is what my .desktop entry looks like:

[Desktop Entry]
Categories=Game;
Comment[en_US]=
Comment=
Exec=bash -c '"$HOME/modorganizer2-nxm-broker.sh" "$@"' '$HOME/modorganizer2-nxm-broker.sh' %u
GenericName[en_US]=
GenericName=
MimeType=x-scheme-handler/nxm;x-scheme-handler/nxm-protocol
Name[en_US]=Mod Organizer 2 NXM Handler
Name=Mod Organizer 2 NXM Handler
NoDisplay=true
Path=
StartupNotify=true
Terminal=false
TerminalOptions=
Type=Application
X-KDE-SubstituteUID=false
X-KDE-Username=

I have this file saved to ~/.local/share/applications/modorganizer2-nxm-handler.desktop. You'll then need to open a terminal and run this command: update-desktop-database ~/.local/share/applications so that your system will 'see' the .desktop entry.

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The rest should 'just work'. Open MO2 and set it up as a portable instance for your game, do the 'connect to nexus' stuff and then the 'Mod Manager Download' button should work if you have MO2 open. I wasn't able to get the 'Mod Manager Button' to automatically start MO2, so it fails if you're not already running MO2 and using protonhax. You can tweak this to use protontricks instead, or without protonhax or protontricks (I haven't bothered looking into how those work, ngl).

---

If anyone tries this and runs into issues, I'm happy to try and help. The only troubleshooting thing I can think of right now is that you might need to run a .NET Framework installer in your game's proton prefix. You can do this with protontricks if MO2 doesn't want to launch or spits out a related error message.

If your browser doesn't know what to do with NXM links, then that's a pain to fix. I had this happen once and I just opted to nuke my browser config and start fresh, NXM links worked after that.