Almost all of it. The only thing it needs to contain is name, whether you are "immune" (vaccinated or natural antibodies), and a signature to verify it hasn't been tampered. When you were born, which vaccine you received, and when you received it are not necessary to show that you won't be spreading the disease.
Some EU countries have restrictions that get lifted after the first shot (e.g. entry to Austria), some after the 2nd shot, some 14 days after the 2nd. So the number of doses, the date of the most recent one and which vaccine (not all countries accept Sputnik).
How does "Name: John Doe. Vaccinated (or 'Immune'): Yes" tell anyone that you, who are flaunting this pass, are the John Doe who is vaccinated? Names suck as identifiers.
