Update error

Are you using a VPN connection, or is your Wi-Fi router blocking the access to Apple?

Any restrictions set up in Screen Time?

Or is your device managed by a company or other institution?

Can you try to update iOS, using your computer?

Update your iPhone or iPad - Apple Support

An update requires both a WiFi signal and cellular service. If you want to update wirelessly, you need to fix that No Service issue first. Otherwise update using a computer as Ingo2711 suggested.

Not necessarily. My old iPhone SE installed it‘s latest iOS 15 update wirelessly, without the SIM inserted.

Some do and some don't, it seems to be random. The ones that do require it use the cellular for verification.