How can I blank my screen now with xset and wake it again?

For an X11 session, try xset dpms force off. That asks the display to switch off immediately. Moving the touchpad or pressing a key should wake it again.

If it doesn't work, check which kind of session you're running. xset controls the X server, so it isn't a general solution for a Wayland desktop.

There's also xset s activate if you just want to activate the X screen saver now. That's separate from DPMS: the screen saver can blank the display, but it doesn't turn the monitor off in the same way.

On Wayland, the command you need depends on the desktop environment or compositor. There isn't a single xset equivalent that works across all of them, so check the options for your particular desktop.