Why is it saying I’m not connected to internet when I am and not letting me update my phone

To update over the air from the phone all of these requirements must be met:

• You need at least 6 GB of free storage
• You must be connected to a Wi-Fi network (and not a personal hotspot)
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN
• The phone cannot be in Airplane mode

If you can't meet all of them you can still update using your computer.

If the above list of requirements has been met, then the next usual reason for this error is a misconfigured Wi-Fi, or a problem between the Wi-Fi router and the internet; with the wiring or the ISP. If you’re in this case, your iPhone is connected to Wi-Fi, but connections to servers off your network are not available.