One obvious one to consider is the diterpenes in filtered vs unfiltered brewing methods. Filtered methods will remove most of these. Diterpenes will help reduce inflammation and may enhance the flavor of the coffee for some, but the ones in coffee are unfortunately also linked to increased LDL (bad cholesterol), so as a drug choice, there's not a clear winner in whether filtered or unfiltered coffee (as in French press, for example), will result in a better black coffee.

From my own anecdotal experience, lower inflammation has a wide variety of cognitive benefits, regardless of the means, while things that increase my inflammatory response (for example, allergies), make it much harder to think clearly.

Side notes: I don't drink milk so can't speak to the lipids that might further influence intake. But even the heat of coffee will have an effect: if it's scalding hot, some of the caffeine will be absorbed in the mouth, and if it's very cold, it'll wind its way further through your system before being absorbed.

I'm just a coffee drinker, so take all of this information with a grain of salt, unless your sodium is too high? Caveat emptor

Polyphenols...

https://pmc.ncbi.nlm.nih.gov/articles/PMC8601035/

That's certainly an interesting thing I wish we knew more about. My qualitative experience is that coffee gives me more anxiety than any other form of caffeine I've tried, including ones that don't contain L-theanine.