ESA-UC: Deductions confusion

Hi. I'd appreciate help with this, if anyone can make sense of it?
Since the sudden mention of CB ESA, after I'd claimed UC, on time...and it NOT being mentioned on any ESA letter I have.......I have not heard anything from ESA since.
I claimed UC in Sept. and during the 2 weeks after that, I received one payment of ESA (usual amount) & my last HB payment from my Local Authority.
I was told (under managed migration/transition) I'd receive any old benefits due during the 2 weeks after my UC claim date, but these wouldn't affect UC payment calculations, & neither would my PIP (both components) be relevant to calculations.
I'm pleased to say that my journal messages informed me that ESA had been in touch with UC, so they knew to put me in LCWRA group - they said this can sometimes take sone time, but they knew now....Phew! No appeal required, I am so tired....
Anyway, I had chosen not to get an advance payment, to wait it out (I don't like debts), but was pleasantly surprised to receive (without announcement or letter) a payment of ESA, into my bank account, which was a sum that's less than the old amount, let's say it was around £250 approx.
This appeared in my bank account two weeks after the "final" ESA payment (paid as usual during the two week post-claim window, referred to above) Also, after the message about ESA having updated UC about LCWRA.
(I am confused, as not sure what this payment is - it's less than old ESA, and not UC, but I assumed it was all unfolding as it should, and I was grateful for some unexpected money).
Then, a letter appears on my UC account, that I'm told to log in to. It says, "you've been overpaid UC by around £400, as claiming ESA plus UC"
I haven't been paid ANY UC yet!
I replied, with panic and confusion, that I hadn't been paid, let alone overpaid - and was told my statement would be issued soon, with first payment made a few days later, in mid-Oct. They said you need to tell ESA you're getting UC - but ESA must know, as they've been in touch with UC (as above), and reduced the payment (as above too).
Now I can see my statement, with a hefty deduction figure (not sure what this is based on) of over £600.
It's an updated statement, I can see the previous, original one only had deductions of approx £240, which would make sense - if that deduction was based on the unexpected ESA payment, received after the 2 week transition period, as discussed above.
I'm so confused - I have asked for clarity, with figures and explanations, but I've got nothing back, just a comment about overpayment, again.
Can anyone make sense of this, or shine a light on what's going on? I still haven't received any UC, but when I do, it'll be minus £600, apparently, and I don't have any idea why!
Thanks in advance

Thank you, but just to be clear - it is the official statement that I'm referring to.
It says I am being deducted over £600 - for benefits I am claiming.
I also received a letter, sent through the UC messaging system, saying that I've been overpaid UC, when I haven't been paid anything.
Other than my usual old ESA payment, which was paid in the 2 weeks from date I made the UC claim (I was told this would not affect UC payment), I have only received one payment of under £300, (during the assessment period of claim date + one month), which I wasn't expecting, as I haven't had any letters from ESA.

So, I am at a loss to know what the deduction of over £600 is for. Any ideas?

I'll try to reply for the second time, the last reply didn't load:

My statement for the assessment period, or 1st month of UC (early Sept UC claim date - early October date) says:

Standard amount - xxx
Rent - xxxx
LCWRA - xxx

Total = ZZZZ

Then it says:

Deduction from ZZZ = £600+ (due to other benefits claimed)

I don't know what the £600+ deduction is for.
I was told that any old benefit payments due to be paid during the two weeks following my UC claim date, would NOT be deducted from my first UC payment. I did receive one payment of my old ESA, due according to the old schedule, ten days after submitting my UC claim.

Then, 2 weeks later - or 24 after my UC claim was submitted - without any notice/letters being received - approx £290 was paid into my bank account, listed as ESA. This was unexpected, and not the old rate of ESA, so presumably new style ESA?

If the next payment of NS ESA is due 2 weeks after the one mentioned above, it will be paid to me after the UC assessment period.

So, I'm not sure why I will be deducted over £600 from my UC first payment?

If the old ESA payment (paid to me 10 days after my UC claim date) should not be considered, and only one NS ESA payment was paid (during the assessment period) - where does the £600+ figure come from - as this is what's being deducted from the first UC payment, apparently.

Does this make sense?