I don't have the time to provide such a detailed answer, but there are a few options.

At least on Sway (and I imagine other wlroots-based compositors) it's very easy to do: create a virtual output and start a VNC server attached to it. Start your vnc client on windows. A comment I posted 5 years ago: https://news.ycombinator.com/item?id=25892128

The comment linked above is on the topic of Deskreen, which is a tool that does that.

Funilly, I also commented something similar there: https://news.ycombinator.com/item?id=34010970 the article explains how to do it on a lower level (pretending a display is connected to the GPU), works under X11 too.

A few days ago, an update locked me out of my server. I used a cheap USB HDMI capture card to use my laptop as a screen, which worked very well: that could be another option.

Then I guess that there is this option, which is new to me. It feels like this could be a toogle in sunshine, somehow :)