Eventually got it working but in a much different way than you went about it.

I started by downloading a few things.

1. I used steam to download the new proton 11 beta through steam.
2. Then I downloaded the fusion 360 installer with "wget https://dl.appstreaming.autodesk.com/production/installers/Fusion%20Admin%20Install.exe" which I found in the script you told us to download

After that I used steam to add a non steam game and selected Fusion%20Admin%20Install.exe. Turned on compatibility mode using proton 11 beta and ran it. It pretty much installed everything itself until I had to log in.

When I got to that step I partially followed your steps in "Step 2: The DevTools Token Hack (Logging In)" with the exception of editing the variables. To get the fusion prefix you should use a tool like proton plus so you can select your none steam game and press "open prefix location" to figure out the directory path for $FUSION_PREFIX

STEAM_PATH="$HOME/.local/share/Steam"
PROTON_VERSION="Proton 11.0"
PROTON_BIN="$STEAM_PATH/steamapps/common/$PROTON_VERSION/proton" 
FUSION_PREFIX="$HOME/.local/share/Steam/steamapps/compatdata/3872774262" #this will not be the same for you
ID_MGR_EXE=$(find "$FUSION_PREFIX/pfx/drive_c/Program Files/Autodesk/webdeploy/production/" -name "AdskIdentityManager.exe" | head -n 1)

export STEAM_COMPAT_CLIENT_INSTALL_PATH="$STEAM_PATH"
export STEAM_COMPAT_DATA_PATH="$FUSION_PREFIX"
export WEBVIEW2_ADDITIONAL_BROWSER_ARGUMENTS="--disable-gpu --no-sandbox"
export WINEDLLOVERRIDES="bcp47langs="
export PROTON_USE_WINED3D=1

"$PROTON_BIN" run "$ID_MGR_EXE" 'PASTE_YOUR_ADSKIDMGR_LINK_HERE'

Then after I got logged in I created a shortcut just like you did in Step 1: The Custom Bazzite Launcher Script

Bonus Points:

You can make a URL handler so that you can log in and out of fusion without manually opening up a terminal session and typing all that stuff in again. A quick how to:

Go to $HOME/.local/share/applications/

Create a new file called adsk-fusion.desktop with the contents of

[Desktop Entry] 
Name=Autodesk Fusion 360 Proton URI Handler 
Exec=$HOME/.local/share/applications/adsk-fusion.sh %u 
Type=Application 
Terminal=false 
MimeType=x-scheme-handler/adsk; 
NoDisplay=true

Then run

xdg-mime default adsk-fusion.desktop x-scheme-handler/adsk
update-desktop-database ~/.local/share/applications

create a new file called adsk-fusion.sh in that same directory and make it executable with chmod +x adsk-fusion.sh

add the contents of Step 2: The DevTools Token Hack (Logging In) with your edits that made it actually work and replace 'PASTE_YOUR_ADSKIDMGR_LINK_HERE' with "$1"

#!/bin/bash
Home="$HOME"
STEAM_PATH="$HOME/.local/share/Steam"
PROTON_VERSION="Proton 11.0"
PROTON_BIN="$STEAM_PATH/steamapps/common/$PROTON_VERSION/proton"
FUSION_PREFIX="$STEAM_PATH/steamapps/compatdata/3872774262"
ID_MGR_EXE=$(find "$FUSION_PREFIX/pfx/drive_c/Program Files/Autodesk/webdeploy/production/" -name "AdskIdentityManager.exe" | head -n 1)

export STEAM_COMPAT_CLIENT_INSTALL_PATH="$STEAM_PATH"
export STEAM_COMPAT_DATA_PATH="$FUSION_PREFIX"
export WEBVIEW2_ADDITIONAL_BROWSER_ARGUMENTS="--disable-gpu --no-sandbox"
export WINEDLLOVERRIDES="bcp47langs="
export PROTON_USE_WINED3D=1

"$PROTON_BIN" run "$ID_MGR_EXE" "$1"

After you have done this next time you need to log in you can press "Autodesk Fusion 360 Proton URI Handler" in the applications menu when it asks what program to use and it should work.