iPad shows weak security error and asks for WPA3

If there is an add-on VPN client app installed, remove it, force-restart, and try again.

Log into and check that the Wi-Fi router or Wi-Fi access point is set to WPA2 AES and not WPA2 TKIP, and—while logged into the Wi-Fi—check for firmware updates from the Wi-Fi vendor, and apply the most current available.

Down-revision firmware can cause issues, and WPA2 TKIP is considered weak.

If the router or access point doesn’t specifically indicate WPA2 AES in its UI and/or its published specifications, it’s probably WPA2 TKIP.

Try a different Wi-Fi network, and see id this issue is isolated to this Wi-Fi router.

If you have already verified the above including WPA2 AES and not WPA2 TKIP, contact Apple Support. They’ll want details of the Wi-Fi setup.

If you are concerned about iPad warnings concerning weak security, or other elements of your WiFi setup, your WiFi network may benefit from update in either settings or improved hardware...

Your iPad is no less secure today than it was prior to the update to iPadOS15/16. iPadOS15 or later is able to [warn] bring to your attention potential security deficiencies of your WiFi network - or other settings that may impact your privacy or security.

This support page describes the more secure (recommended) settings for WiFi:

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

It is possible that your WiFi Router is too old to be (or not capable of being) configured for more secure settings. As such, you can either configure the most secure settings that your Router will support - or replace your Router with something more advanced that provides better security configuration options. 

Whilst WPA3 is the newest standard, you should aim to use WPA2 (AES-PSK) as a minimum. Some Routers seemingly continue to support the insecure/deprecated TKIP standards - even when apparently configured for WPA2 operation; TKIP will definitely cause a security warning to appear. Be aware that if you are using a WiFi network extender, these may continue to use weaker security standards - and continue to trigger a warning.

There is a also new privacy feature included within iOS/iPadOS14/15/16 that hides your physical MAC Address - and instead uses a randomly selected Private MAC Address. This feature can be enabled/disabled on your iPhone/iPad for each configured WiFi Network. This feature also has bearing upon the appearance of the Weak Security notifications.

More information about this new feature can be found here:

Use private Wi-Fi addresses in iOS 14, iPadOS 14 and watchOS 7 – Apple Support

If you are unable to employ more secure security settings on your WiFi network, you might consider replacement of your WiFi network equipment, such as your WiFi Router, with more advanced equipment. However, if the router is provided by your ISP, this may not be practical proposition. A potentially cheaper and more flexible approach might be to add an additional upstream WiFi Router, of WiFi Access Point (AP) that meets the required standards.