My wife and I both have S22's. We both installed the new One UI update within the past day. Now wifi connectivity is broken. Some networks are fine; others, including our home wifi network, no longer have any internet connectivity when the phones are connected to it. They say "'connected without internet."
I have reset all of my wifi hardware. All of the other devices in the house on the wifi (smart TV's, game consoles, laptops, etc) have no problem connecting to the internet on our home wifi. It's only the S22's that fail, and only since this update.
All the results I can find about this problem are from back in March-April, and none of the solutions (turning airplane mode on and off, trying to switch to static IP or Phone MAC versus randomized MAC) work. Samsung has somehow reintroduced this problem in One UI 5.
I have no issues with my S22 Ultra and WiFi. Have you forgotten the network and retried logging in? Also try going into recovery and clear the system cache and repair apps.
Not sure then unless the update caused your phone to not like some setting on your WiFi. You said they connect and have internet on other networks but not yours. Have you reset your router to factory and see if this fixes your issue?