No server is involved in scanning/verifying the QR codes, the only privacy violation would possibly be the people scanning the code taking the name/DoB for themselves but that would be a GDPR violation and I'd guess no legitimate business would try that.
I'd be showing my ID/vax record to those restaurants either way so it just seems like a technicality in the end. If you don't like it, don't use it, like all covid apps in the EU.