This could use some clarification. Do you mean that you want...

• Lutris or Plasma (depending on a detected game controller) to automatically launch as soon as your computer finishes booting, instead of the display manager that normally presents a login screen?
• Lutris to automatically launch when you log in to a Plasma session while your PS5 controller is connected?
• Lutris to automatically launch whenever you connect a controller while already logged in to a Plasma session?
• Something else?

The possibilities really depend on what you're after.

Certainly seems like you could make a udev rule to do something along these lines, I know you can execute specific commands /w udev, whether or not you can enable or disable a system service or whatever, I dunno, guess you could always execute a custom start script before WM that decides which WM to start

I think the bigger hurdle here is that you need to do some legwork and research, else you would not be here asking this question 😉

It's possible but then I'd ask why? What's the purpose of booting a different DE based on the controller type?

Do you mind explaining the incentives, why would you want a different controller to boot different things like that?

I think you'd be better off just having a controller hook up and that triggers a bash script to start steam in big picture mode or lutris.

You probably could do something like this if you really wanted to but this would be clunky. If you're always turning off the machine after you're done using it, maybe it'd be OK but IMO, it would make more sense to just use KDE plasma and script something to get the functionality that you want.

You wouldn't have to worry about booting things up or shutting them down if you wanna switch between gaming and whatever else, you could easily make changes to it, and it'd likely be less complicated.

Hell even a shortcut that opens it through a button combo or something would work for this. Pair controller, hit a key on your keyboard, boom, steam opens. That can be done through KDE natively through the shortcuts settings. Very easy to setup and something I use a lot.