Yes, KDE is a desktop environment. It's one of the "Windows-like" ones and very customizable, and arguably the most technically advanced one at the moment.

Wayland is the display server, as it is called. It's basically the back-end component that facilitates actually displaying anything on the screen. It replaced another component called X11, which was released in 1987 and had become a completely unmaintainable mess of technological debt.

Wayland took a very long time to develop and there are still some growing pains, which is why you will occasionally still see people arguing that X11 is better -- these days you should probably just ignore anyone who says that though, as the overwhelming majority of users will be much better served by Wayland than by X11.

As for what distros support it, basically every up-to-date distro (latest major version release during or after 2024) using one of the following desktop environments will default to Wayland: KDE, Gnome, COSMIC, Sway, Hyprland. Other DEs don't yet have stable Wayland support. Notably Linux Mint, a very common recommendation, is not on this list because the Cinnamon DE it uses does not yet support Wayland.

A couple of example distros mentioned in the thread and article would be Bazzite, Fedora and CachyOS. These distros all update swiftly, which is desirable because the Linux desktop is advancing very quickly at the moment. Slower-moving distros like Debian or Ubuntu LTS tend to miss out on a lot of nice new features.