People say you cannot eat anything before davening shacharis. What is the actual source, and how far does it go?

The Gemara (Berachos 10b) learns it from the pasuk “you shall not eat with the blood” (Vayikra 19:26), read as do not eat before you pray for your blood, and it says one who eats and drinks and only then prays is like casting Hashem behind his back. The Shulchan Aruch (Orach Chaim 89:3-4) paskens no eating or drinking before davening, but plain water is fine even on shabbos, and anything medicinal is fine. And then it says something people seem to skip: someone who is hungry or thirsty is in the category of someone sick, so if he cannot concentrate he should eat or drink first and then daven.

So the questions:

1. If the Shulchan Aruch itself says a hungry person who cannot concentrate should eat first, why is “no food before davening” treated like an absolute rule? Is the heter only for someone literally shaky, or does it cover anyone who davens better after eating?

2. Where is the line between water and everything else? On this site, coffee with milk before shacharis was answered “certainly”. Does that extend to juice, a protein shake, a full breakfast?

3. Does it matter what part of davening? Is eating before birchas hashachar or korbanos different from eating before shemoneh esrei?

4. Bottom line: for someone who genuinely davens with more kavana after breakfast, is eating first the right thing to do, or a bedieved, or still assur?

Basically, what is the real rule here, and how does the concentration side actually work?