I’m not a scientist but I suspect it’s probably difficult to directly attribute a single observation to climate change. What you want to look for are trends, so I’d say the best thing to do is keep observing (including common species) and getting the data onto iNat. Also annotating observations will help generate phenological data. iNat observations were used in an attempt to model off-season Yucca blooms [PDF], for example.
Another approach might be a project like this one that @leptonia made last year, which collects fungus observations from areas affected by Tropical Storm Hilary (a storm which was possibly made more likely due to climate change).