How to go about deciding the acidic strength of a functional group in an aromatic compound?
This question is, at best, flawed. The most acidic protons on the structure provided are not any of the labeled OH protons. Rather, the most acidic position is the one I have drawn a rectangle around below.

Deprotonation at this position produces an anion with a resonance contributor in which both rings are aromatic. The circa 150 kJ/mol resonance stabilization for each ring will vastly outweigh any delocalization that might occur for the oxyanions formed by deprotonating any of the OH groups.