LCWRA reassessment and backdated payment

On Aug 18 2021 I was reasessed to LCWRA prior to that I was on LCA from Aug 18 2019. I asked  in my UC Journal to be re assessed first in Aug 2020, then Again in October 2020 , and again in November 2020. At the end of December 2020 I received a reasessment form which I submitted early Jan 2021. In late July 2021 I  reasesent interview for LCWRA and  around a month later August 18 21 I was then informed I'd new moved into the LCWRA group and should receive a payment sometime. I then had the first  payment l around Sept 18  2021. As I had to wait so long after making the application should my claim be backdated to when I submitted the form eg in Jan 2021. I did ask about this and I thought they said I should get a backdated payment around 3 months after. I have telephones again 4 months after my first inquiry and their response was
"I'm  not Due any backpay becuse it's a reassessment,  it states my new rate should already be included in  my universal credit payments (which is £340 something).which I I was awarded 18 Aug  21   they also stated limited  capability for work has been awarded and the relevant period does not apply as this is a review of a previous decision in which the right pay has already been served" so after I guess I won't be getting a backdated payment from when I first submitted the UC50 form in Jan 2021 to when I was actually put into the LCWRA group and re-assesed in Aug 2021.  It doesn' make sense or sound fair?