A proper answer to my question. I had been looking for 20 mins online for an idea where they saved. You’re the first to infer that it simply does not leave iMessage/messages
After I copied the audio in text message , and pasted it in files I renamed my Audio message . I went back to messages and at the top searched “audio” and mine showed up , including the one I renamed. You can search the name also if you give it one
