FWIW, it is not an Intel thing. I got an Asus G14 2021 which has nothing Intel (Amd CPU and nvidia GPU) and this does not support S3, only the modern "connected standby" crap.
Talk about ruining a perfectly working solution for almost no gain.
I generally add custom application shortcuts to XFCE's keyboard preferences instead of i3's config and change i3's $mod to the Alt key. Haven't had any problems of conflicting shortcuts.
I do this with XFCE and it works really well. You just have to prevent xfce-panel and xfwm from starting up and autostart i3 instead. Replacing i3 with xfwm on the fly also works like a charm, I can toggle between tiling and floating WM's using keyboard shortcuts.