I think One UI 5.1.1 update is for foldables, tablets or maybe flip phones whereas One UI 5.1 is for phones like S23, S22, A54, A53, A73, etc. So you won't get One UI 5.1.1 update on your S22 Ultra. You get Android 13 One UI 5.1 not 5.1.1. If you already have Android 13 One UI 5.1 installed on your S22 Ultra then you should expect Android 14 One UI 6.0 (not 5.1.1) as the very next big Android update.
Yeah, on Google, they say S23, etc..... will get One UI 5.1.1, but actually, it is One UI 5.1 because S22 is not a tablet, fold or flip phone. Your phone should be receiving a big August security update, which may have a size of over 1GB, which I think it is the one websites are referring to as one ui 5.1.1. Some countries are getting the update first, and some countries will get it later (Its how the updates are rolled out). Watch this video to see what features you may get in the August security update (It doesn't matter if the video is made for S23 Ultra but it should be nearly same for S22 Ultra)