All biometric passports have serial numbers that change when issued. Per this notice from the Singaporean government, this is an ICAO requirement: https://www.ica.gov.sg/news_details.aspx?nid=12246
And since virtually all passports are now biometric, even those countries (like Singapore) that did not previously change numbers do so now.
Update: Here's Document 9303-4 "Specifications for Machine Readable Passports (MRPs) and other TD3 Size MRTDs" direct from the ICAO Machine Readable Travel Documents Programme:
Field 05/I (Mandatory)
As given by the issuing State or organization to uniquely identify the
document from all other MRTDs [machine readable travel documents] issued by the State or organization.
"Uniquely identify the document" means that the number cannot be reused for other documents. And of course it's only a "recommendation", because ICAO only sets standards and does not enforce them -- but if countries produce passports that don't follow the rules, they're not going to be accepted by other countries. In particular, ICAO member states are supposed to ensure that non-MRP passports are no longer accepted after November 24, 2015.
And a final nit: the standard above is technically for machine-readable passports, which is not quite the same thing as biometric passports, but the standard in question does document the rules of biometric passports, and all biometric passports are supposed to follow the rule above.