Oh btw, i have a theory what the other sounds could be.
So, if the UA is a Communicator and we have identified the Morse...well...lets take a look at the past.
We Humans have send Morse into space, right? And we have found Morse inside that chittering that we can translate.
Thargoids obviously use another language, and i have read somewhere that they use an Octagonal system, and someone back then tried to find an Octagonal system in that purr (i think he found it, but couldnt decode it).
So what about this:
The Chittering is OUR Language, the Purr/scream is THEIRS.
They want to teach us their language, they point at something, chitter it in what they know from us, and tell us what it is called in their language.
So if we analyze both of them and create an Thargoid alphabet based on that, would that make sense? I mean...translating a new language is hard work...but maybe it is worth a try
Additional idea:
From what i have seen, voyager transmitted in different languages, also that
golden disc had several informations on how we count and all those things.
So maybe the UA is like our Voyager - it sends in morse to tell us that they have understood our message, and now they are sending theirs. Maybe the sound is not just "one big code" but several smaller ones?