What does “Sautéed” mean in “Someone who has not sautéed in a subject”?

This phrase is not common, and appears to just be a diversion into cooking terms to create an analogy.

Sautéing is as you defined it. When you sauté olive oil, garlic, and onion together when starting to make an Italian pasta sauce, the outcome is that the oil will take in the flavor of the garlic and onion.

So, by analogy, Paul Ryan has not taken in the flavor of foreign policy, i.e. he is inexperienced in foreign policy.

Readers will probably understand this analogy if they understand the more commonly used analogy of marinating.

The idea of sautéing is "to ensure the ingredients have been thoroughly jumped" (tossed).

"all the ingredients are heated at once, and cooked quickly. To facilitate this, the ingredients are rapidly moved around in the pan" (wikipedia).

Speaking of Paul Ryan, the writer explains, "till now, his idea of a border dispute has more likely involved Wisconsin and Illinois.” He has not trained himself thoroughly and quickly on the Middle East and ME policy while at Capitol Hill. So "is no Middle East savant".

The author is known not so much to use idioms and metaphors as to set precedents with her own creative ones.