Last time we visited Uzbekistan, breakfast was a buffet, so most guests with dietary requirements were able to select suitable items. It’s worth noting though that hotels/restaurants in Uzbekistan were not able to obtain dietary products, such as gluten free bread. The evening meal was a set menu. At some of the restaurants, the staff were happy to provide something separate (e.g. a meal without gluten) but they often didn't understand dietary requirements in the way that a UK restaurant would (so they may not have considered cross contamination, for example).
For the flights, Uzbekistan Airways offer categories e.g. vegetarian or gluten free. You can check the full list on their website. They aren't able to offer specific meal requests that don't fit in one of their categories e.g. vegetarian with no onion. We will choose the category that we think matches closest with your dietary requirement but please let us know if you have a specific request (e.g. if your diet is gluten free and vegetarian you can let us know if you would prefer the gluten free option or the vegetarian option, otherwise we will choose one of these).