Hibernate is all in the kernel. You trigger it by writing to a file in /sys. Your DE choice has nothing to do with this.

Most things on Linux are actually like this, where everything is in the kernel or some other small project and the DE just adds a wrapper GUI (or sometimes a management deamon) and really has absolutely nothing to do with how the thing works.

And thank goodness for that because all of the popular DEs use terrible window managers. I wouldn't bother with X11 if those were the only functional choices.

Also some people (like me) really don't mind tearing but can't stand an extra frame of latency when we're typing. It's nice to have options since no one agrees on everything.