Their letter means you are at the "Enforcement Stage". After this, if you do nothing, the bailiffs will visit your property and charge another fee of £235. Both their fees are statutory, and cannot be varied.
So with no visit fee, our recommendation is normally to pay the amount demanded. You can then, and at the same time, prepare and submit an Out-of-Time Statutory Declaration that you didn't receive the PCN. The problem with this is that OOT submissions can be objected to, by the council, who invariably do so, on the basis that all statutory enforcement documents were sent to the address as provided by DVLA. So you need a good reason to refute this. Your house move of 2023 is much later that the alleged contravention date, which has to be served within 28 days. So was the address on your V5 on or around this time up-to-date. I ask, because the most common reason for non-receipt of PCNs and subsequent documents is the address on the V5 is out-of-date.
You could ask the council what address they used to serve the PCN and following documents. I suspect this is the key to your problem. Sometimes a minor error in the address is overcome because the local postie knows the address and can mitigate small errors.