'This confirmation only indicates that ...this is the responsibility of Bristol City Council to confirm'.
Means what exactly?
Anyway, trying to piece together the info, you drove inside the zone on 2 days without paying the tariff. You received 2 PCNs, ***2159, ****3304.
So, how did you pay the first, ****2159, and, if using WordPay, what confirmation, if any, did you get from BCC.
Do both of these appear as debits in your bank account, you haven't mentioned neither have you referred to this is your correspondence?
According to the Traffic Penalty Tribunal website, the next stage for the council would be to issue an Order for Recovery which would include a Witness Statement which you could complete to reset the process back to the PCN stage. It is important that this is a Witness Statement rather than, as in London, a Statutory Declaration, because a WS allows you to reset the process to the PCN stage(i.e. the Charge Cert and OfR are cancelled) if you declare that you paid the PCN.
https://www.trafficpenaltytribunal.gov.uk/appeals-process-bristol-clean-air-zone/Follow the links.
Therefore, you don't need to argue with the council at this stage, just wait for the procedure to progress.