"A lot of people"? How many people use this resolution?
What API does "Fast Burst Camera" use? Presumably not the original, long-deprecated Camera API, but might it be using CameraX? Because if it is using Camera2 as well that would prove that the restriction isn't the API - though it wouldn't tell you why Open Camera thinks the device doesn't support it. But Open Camera is, as the name says, "open": if another Camera2-based app gave you the resolution you want you can find the Open Camera source on Sourceforge and see whether you can work out the cause and make your own version (the code is available under the GPL V3 license). Or ask the developer if they have any ideas.
Of course if Fast Burst Camera uses CameraX then it could be a difference between the APIs, or how those APIs interact with elements lower in the stack (of which there are several layers). Getting into that will require a lot more effort, and most likely rebuilding the operating system on your phone from source (assuming you can identify where in the source the confusion arises). I think it unlikely that there's some config file sitting in some system directory that you can just add a line to and reboot the phone and it will work (though as my s21 isn't rooted I can't prove that).
(For what it's worth I don't think it is that Camera2 itself simply doesn't support this resolution: we've already established that it's available on other devices that use Camera2, which is actually pretty old. But it's conceivable that different APIs see the device slightly differently, so if the other app uses the more recent CameraX then that might be the answer).
Before we get ahead of ourselves, I suppose you have tested that 176x144 works in Fast Burst Camera? I just like to cover all of the bases.
There are a lot of assumptions here, but if Fast Burst Camera does work at that resolution and does use Camera2 then probably the simplest way forward would be to contact the Open Camera developer and ask them whether they have any idea why Open Camera does not offer this same resolution on the same device?