It sure seems like a privacy disaster. How could you say its not?
between eu member states, the acceptance of e.g. sputnik-v (the russian corona vaccine) varies. having the name (or id) of the vaccine in the code allows countries who don't recognize a given vaccine to validate codes issued by other eu nations, who are more open to such a vaccine. (what a horriblly worded sentence, i hope you get what i'm trying to say)
That seems reasonable; it's totally plausible that a future variant defeats a vaccine, and at that point you would want to be able to detect people who'd been given that one.
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.