Diet affecting mental health is kind of a no-brainer (see what I did there?). The most extreme case I can think of is epilepsy which in severe cases is treatable by putting the patient on a 'keto' diet. My take on that is that diet affects the blood-brain 'barrier', which isn't a solid barrier at all but an interlocking set of epithelial cell astrocyte and microglia actions (mostly ionic pumping and permeability). This all takes micronutrients to work properly. Shorting those (which a diet of manufactured foods almost certainly does) leaves your CNS unprotected — and for epileptics that means GABA and glutamate aren’t regulated properly, potentially resulting in seizures.

That said, I would suspect the people who mostly eat 'savoury snacks' are also insulin resistant - so they have glucose spikes that come down slowly simply because their muscles have become resistant to absorbing/storing glucose - possible to the point of their astrocytes (same GLUT4 receptors, unclear if they have the exact same cascade that leads from insulin at the cell wall to glucose receptors poking through) might also be becoming insulin resistant - and neurons rely on astrocytes to convert glucose into lactic acid for them.

It's an interesting area.