Linux

It depends:

The traditional DEs (KDE, Gnome and Cinnamon) already have their own screensavers.

The newer ones have coalesced around an extension to wayland called "ext-session-lock-v1":

This protocol allows for a privileged Wayland client to lock the session and display arbitrary graphics while the session is locked.

You can see support for it here: https://wayland.app/protocols/ext-session-lock-v1#compositor-support

It's on basically all the new ones except where it doesn't make sense, such as:

• Gamescope (designed to keep a game fullscreen at all times)
• Cage (for kiosk machines, basically gamescope but for interactive maps in shopping malls)
• Weston (the reference wayland compositor which should have protocols that everything uses, I'm not sure how useful it would be to add screensaver support to the reference implementation then have it popping up on in-car-displays when you're trying to follow a map while driving)

Everyone who needs it has it already.

There will probably be an ext-session-lock-v2 and get pulled into the traditional DEs at some point, but probably after a whole bunch of getting everyone around the table and in agreement on some security questions: how do we prevent malicious software setting themselves as a screensaver for a screenjacking attack?, what happens when the screensaver crashes?, that kind of stuff...