Whoever wrote the regulations was an idiot, but councils must obey the regulations, and those regulations do not permit them to claim the toll charge on the PCN, as was stated in 2018, by Caroline Sheppard, the Chief Adjudicator of the Traffic Penalty Tribunal. However, as far as can be made out, this ruling has never been tested since. I see they have re-offered the discount, so it is now your decision whether to take them to TPT or pay up. If it were me, I'd be going to the TPT, but it's your money not mine.
Interestingly, the Birmingham CAZ Order specifically states that payment of the PCN discharges the toll charge debt. Their lawyers are obviously more up-to-speed than Bristol's.