Windows by default doesn’t fully power off when you tell it to shut down. It goes into hibernation and keeps the network open for updates and will sometimes power back on to complete these updates.
If you want to fully power off, hold the left shift key when you click shut down. Or turn the power off elsewhere (eg. psu or power bar.) I’m sure there’s another way to do it, or to prevent the behavior entirely.
Fast boot is just Windows logging you out of your session, then hibernating.
Sleep is keeping the computer in a low-power state with RAM powered on…
Both of these have been known to result in laptops powering on unbeknownst to their owners to perform updates and remain powered on afterward.