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.
The issue is that customs agents have the authority to refuse you entry into the country for no reason if they so choose. Refuse to consent to a search and you could be refused entry. This includes simply transiting through the airport, as the US requires foreigners to go through customs even for connecting flights (I’m not sure if that’s always the case, but it has always been the case for me.) So they can’t force you to let them search your phone, but the end result is the essentially the same.
Someone posted a guide on Steam forums to get it running under linux. You can check it out here https://steamcommunity.com/sharedfiles/filedetails/?id=2044037599
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.