> Am I understanding correctly that I still can't run a headless session on my VPS in a way that let's me use remote control for a better 1st party mobile experience that doesn't require my laptop to be awake?

What exactly are you trying to do here? I have codex running on a VPS (headlessly) and I can use it just fine, ssh into the box and do "tmux attach" or whatever you use for such things. Where does your laptop come into play here and how is it related?