iPad air 4th generation won't connect to wifi after update 16.1

Start with basic WiFi troubleshooting - as detailed here:

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support

Recommended settings for Wi-Fi routers and access points - Apple Support

If your WiFi has been set-up according to Apple’s recommended settings, WiFi and Internet connection difficulties are usually an indication that your device does not have a routable IP Address - your IP Address usually being assigned by DHCP. When this occurs, your iPad may only have a self-assigned link-local IP address that begins 169.254.x.x.

System software updates can, in some circumstances, trigger a problem with the iPad (or iPhone) internal routing table. The causes are many, but are usually attributable to some types of App or associated device configuration.

If you have a VPN App or profiles installed, or a security App such as Norton, these may be interfering with DHCP - and preventing your device from obtaining a valid IP Address for the WiFi network/hotspot to which you are attempting to connect. The resolution is usually simple; if installed, you may only need to temporarily disable or remove the Security App and/or VPN.

DHCP is frequently used to automatically obtain an IP Address. Until your iPad has a valid IP Address to connect to your network, you will not have an internet connection. Disabling or removing VPN and/or the offending security App should allow DHCP to operate normally - allowing connection to your network and the internet.

If this resolves your issue, the VPN and/or security App can be reinstated after the connectivity problem has been resolved.