ATMs could OCR and log the serial numbers of bills they dispense, and they obviously know who they're dispensing to. Banks could do the same with incoming cash at the end of the business day.
The tracking would be weaker than with electronic payments since some notes will be re-used after being given as change, but it'd still be useful to a government that wants to track its population.
The banknote recovered was passed to the Bank of England, who were asked to trace where it was issued.
Detectives learnt it had been sent from its printing works to the Leeds branch of the Bank of England, just a few days before the murder.
https://www.manchestereveningnews.co.uk/news/greater-manches...
Indeed this is an issue that bothers me since some years. We should indeed think about ways to "reanonymize" the cash (even) more.
Most paper money has a serial number that could be tracked for following the chain-of-possession for that piece of paper.
In the case of Germany I can see a law being written that would require serial numbers be recorded for person-to-person cash exchange. Those guys love regulation. :)