So, no. Lowering the texture streaming pool did not fix the issue. It seemed to make the warning disappear for a few minutes (I lowered it from 8192 down to 6144), but the issue came back and has been a problem ever since. I'm guessing that making any adjustments to your graphics settings will flush the memory and make the error message disappear temporarily. My guess is we need Epic to notice the problem and fix it. It's probably a memory leak.
Correction* I had increased the texture streaming pool size too high (to 8gb out of 12 on my GPU).
I thought you could set it to any value you want, but this is not the case. You shouldn’t increase it more than what you need, because it seems to reserve that memory for the texture streaming pool. Then you end up with less GPU memory for everything else. I thought it wouldn’t use more than it needed, but apparently not. I originally lowered my streaming pool to 6GB and it didn’t solve the error permanently, but I lowered it even more to 4096 and it seems to be a good balance (though according to the warning in my level, I could set it to 3072 and still be fine, but I wanted some wiggle room).
Thank you @TactileVisions for the solution.