Download the Homecoming Launcher
On Steam click on library>add Non-steam game to my library
Browse: browsers typically download to Downloads in your Home directory. select hcinstall.exe
Click add selected games to my library.
Find hcinstall.exe on the list, right click, go to compatibility, click force use of specific Steam Play compatibility tool, select Proton 8 or 9 from the dropdown box. close the window
Click on play for hcinstall.exe. Steam may take a moment to download the proton version you selected.
It will run through the installer, you can leave it all as the defaults.
when you see the launcher you can close it.
right click on hcinstall.exe. click properties
You can change the name in the topmost box of Shortcut to whatever you want (i.e. City of Heroes or Homecoming) this is the name you will see on your library list going forward.
Click Browse next to the box for Target. Go to ~/.steam/steam/steamapps/compatdata/(the folder with the most recent date)/pfx/drive_c/Games/Homecoming/bin/win64/launcher.exe click open (if you don't see .steam when the window first opens tap the gear for settings and select show hidden files, or ctrl+H if you have a keyboard) (~/btw stands for /Home/yourusername/)
Highlight the beginning of target up until the word Homecoming, copy and paste that into Start In.
Close the window and relaunch the game from Steam.