Norway still isn't accepting Americans with vaccinations from the U.S. They are VERY specific about only accepting EU-integrated/valid Covid certificates.
From these pages from the Norwegian Directorate of Immigration and their public health authority:
All EU/EEA countries
If you are fully vaccinated against COVID-19 or recovered from COVID-19 during the last six months, you can travel to Norway now if you can provide documentation for this in a verifiable way. You must be able to:
present a Norwegian, Swedish or Danish COVID-19 certificate with a QR code that can be verified by the Norwegian authorities, or present a COVID-19 certificate following the EU rules for digital corona certificates
You can travel from any country if you can provide documentation for one of the requirements listed above.
The site is very specific that U.S. certificates do not fit the bill.
Countries outside the EU/EEA Area
COVID-19 certificates from countries outside the EU/EEA Area are not accepted as documentation.
Further, from the Norwegian public health authority :
Currently, only presentation of a COVID-19 certificate (Norwegian, Danish, Swedish or EU digital COVID certificate) with a QR code which can be verified by the Norwegian authorities is considered to be a secure and verifiable way of proving vaccination or previous illness. More information about the COVID-19 certificate:
Verifiable COVID-19 certificate (regjeringen.no, in Norwegian)
See your COVID-19 certificate (helsenorge.no)
Here,s the page within that same site that makes it clear that Norway is not yet accepting American tourists
Can I travel to Norway now?
Most people cannot travel to Norway now
If you live in a country outside the EU/EEA, you cannot travel to Norway now unless you fall under one of the exceptions listed below.