Xbox One fan keeps coming on, even if console is turned “off”.

If you want the fan to stop coming on, yes you will need to change the power settings to power saving mode.

No, the xbox has the fan at full power even when sitting idle. I’ve also tried restarting the xbox multiple times or even not playing at all and waiting for tomorrow and without failure, the fans still kick in loudly

one weird thing is that after i turn off the xbox, the fan is still whirring at a fairly high speed... some would say it is the excess momentum of the fan, but firstly if i unplug the main power source to the already off Xbox, the fans instantly come to a halt
and also, if i wait around 3-5 mins after i turn the xbox off the fans would instantly come to a halt.

I've had the freezing issue, where it just freezes out of nowhere and the fan does continue to go. I've had issues where I turn the Xbox off but it keeps running. Visit this link:

support.xbox.com/.../console-turns-off-unexpectedly

Perhaps you need to replace your power supply even if it looks to be working fine?

do you have your console on instant mode if so your Xbox one fan should turn off if you have your Xbox one is on energy saving mode it should turn off within 5 minutes

I've changed my console to energy saving mode, and I the fan now turns off. Thank you for helping!

If the console is turning off then this is usually due to overheating (the console does not need to feel hot or the air coming out of it as the overheating occurs between the heatsink and the chipset), The fan will always speed up if the system detects that
the hardware is getting too hot.

You could try the troubleshooting article for the console unexpectedly turning off, other than that if it keeps happening then you would need to register it for repair.