How to find the state of the art algorithm for a specific problem
I generally go through review papers in the field and try to cite them as well if they have any sentence in the paper &quot;claiming that the previous method is SOTA&quot;.
There are also benchmark sites.
Famous datasets even have their personal benchmarks linked to their sites.
You could use research gate or any other forum and ask a question there.
You could try a keyword search on google scholar and see if any paper claims to do so.

Regarding the difference in setting, generally the &quot;well-acclaimed&quot; SOTA papers don't have these issues. At least that's what I've noticed majorly in my field.
If that is the case, then I suggest making a small study within the paper covering all the results in the different settings. (Please do correct me if I'm wrong here).