My answer in

• https://www.reddit.com/r/AskHistorians/comments/iibcoz/how_comes_east_asia_is_not_known_for_dairy_but/

covers the dairy products. They are mostly or all not of Turkic origin.

The bread and rice dishes are also not of Turkic origin. The reason is similar (but without the complication of lactose intolerance). Wheat was domesticated in Western Asia, and bread spread with the cultivation of wheat. Rice was domesticated in China, and spread. It's very unlikely that dishes like pilaf are of Turkic origin, since the western spread of pilaf appears to date to the Abbasid period, and is likely to be descended from older Western Asian dishes using wheat products like burghul. Dishes like this are not hard to invent either, as seen by probably-independently invented dishes in West Africa (where rice was independently domesticated).

Meat dishes such as souvlaki and meatballs are certainly not of Turkic origin (although they may have been independently invented later by Turkic peoples). Dishes like souvlaki were being cooked in the Mediterranean area by the early 2nd millennium BC, and meatballs are known from ancient recipes from Europe to East Asia, long predating the Turkic expansion (and therefore long before there were Central Asian Turks).

Pashmak and nougat are probably Persian inventions, and thus Central Asian, but not Turkic (although the Chinese claim priority for pashmak-like candy). The names at least are of Persian origin.

This allows a simple answer to your question:

How come they were able to create such great foods in other lands but not back home?

Turkic peoples adopted such foods from other peoples as they spread from their old homeland. Not Turkic inventions, but Turkic adoptions.

You say you read a theory with quite extraordinary claims, then only list some foods and ask why. Not mentioning the theory itself makes it really hard to comment on.

Quite frankly, the list reads a little like 'they invented yoghurt, wheat bread and grilled meat, so any near-eastern, middle-eastern and Indian dish that features any of those was invented by them'. Which would be a... pretty questionable take.

Lastly, it's good to be wary of sources who make pretty wild claims, particularly along the likes of 'ethnicity X invented EVERYTHING'. They may very well be (ethno-)nationalists (in this case perhaps panturkism?), stretching the truth or outright making stuff up to fuel their narratives of superiority.