Difference between 'eat soup hot' and 'eat hot soup'

I'm not a grammar expert, but here are my thoughts on this:

In the first sentence, "most kinds of soup" is the direct object, and "hot" is a phrase of manner depicting the way you eat the direct object.

What do I eat? -- Most kinds of soup

How do I eat it? -- Hot

In the second sentence, the direct object is "most kinds of hot soup", where "hot" is an attribute adjective for "soup". Furthermore, here, "hot soup" is a phrase in itself, designating soup recipes that are usually consumed hot.

What do I eat? -- Most kinds of hot soup

My take on this is that both have different meanings as a result of taking subsets of things (soups) in different orders.

The first "I eat most kinds of soup hot" means I take a subset of soups (one which I eat) and tell you that the majority of these are hot. You imply that you might eat a few cold soups, but most are hot.

The second "I eat most kinds of hot soup" tells you that out of the hot soup set, you will eat most of these. It tells you nothing of how much cold soup you might eat. You could eat most of your soups cold (but still eat many variaties of the hot ones) or not have any cold soups (only eating most types of hot ones).

It is a matter of emphasis. In the two examples you give, hot acts differently.

I like soup hot emphasises that you prefer the soup to be hot, to having it cold.

I like hot soup is indication that you do like hot soup, but you are not stressing the fact that you prefer it to be hot as opposed to cold.

Someone might say something like "I had some wonderful cold gazpacho soup, at Nicola's party. I like hot soup, but I am especially partial to Nicola's cold gazpacho".

Your friend might respond with "I like soup hot" - which would be indication that they did not think much of having cold soup.

In my opinion, it is related to the relative clause.

The first sentence can be rewritten as 'I eat kinds of soup (which is) hot'.

Then, the second one is just a normal sentence.