Huh, today I learned "falsify" has two meanings!

This is not correct. It’s been proven using electron microscopes that generic photosynthesis uses a quantum mechanical process inside every chloroplast. As a photon lands inside the microstructure an exciton hops through a superposition-network of chlorophyll molecules until it finds the low energy reaction center where it splits a water molecule into charged ions, used in further processing. This photon to ion process is nearly 100% energy efficient which would be totally impossible without the biochem exploiting quantum effects at room temperature.

I believe that it is very hard to capture these types of effects because measuring quantum systems impacts them, but I think (fully speculatively) it’s a matter of before we find more and more biochem systems that exploit quantum mechanical effects.

The quantum considerations have more to do with the molecular level. There are definitely quantum effects and considerations for what's happening at the level of enzymes and chemical reactions and they might matter with neurotransmitters at the synapse, and if they matter those effects could be amplified to neuron scale electrical impulses. There could be quantum effects that play a key role in sensory perception (we're talking the level of photons and molecules here too). You have to remember that biology is incredibly ordered and very physically small things matter so all these effects are on the table. Do they actually matter? Unknown it's complicated (outside of a few enzymes and systems where basic things like tunneling are clearly happening)