It's interesting that all of this is in there. In the Netherlands the health minister has multiple times promised that the checking party (like pub/work) would not be able to determine if you were OK because of vaccination, recent negative PCR test or recovered.
Maybe that is only for the national check and not EU passport.
You are correct. The national/intra-jurisdiction checks usually give you a thumb up / thumb down without context.
The cross-border credentials provide context to allow the destination to make a determination if they wish. For example, some jurisdictions may not recognize Sinovac. Others may not recognize a COVID recovery + 1/2 dose series as valid. In the future, some vaccine series may need a 3rd dose.
Each place in different. Some US jurisdictions adopted a "hold my beer" approach. Others have tight standards and vaccine registry, others have good immunization processes, but the integration with third parties is poor.
The Dutch app will have two QR codes: a national one which does hardly contains any information - initials and day/month of birth - and the EU DCC which is discussed here.
Maybe that is only for the national check and not EU passport.