Update

Make sure that:

1. You have a good WiFi connection
2. You have a 50% battery charge or better (and preferably connected to power).
3. You have 6GB of free storage space.
4. You are not using a VPN.
5. Low Power mode is off.
6. You don't have a beta profile on your iPhone.

The go to Settings > General > Software Update.

Signing into iCloud has nothing to do with updating your iPhone. As I've said twice, turn off your VPN.

Turn off your VPN.