Breakthrough infections of fully vaccinated people do occur, but they are rare. RTL found out the numbers.

Of a total of 370,000 fully vaccinated people, 1,381 were infected with Sars-CoV-2.

There are differences between the different vaccines. People who got the Moderna vaccine are least likely to be infected with 0.18%, while Pfizer, the other mRNA vaccine, is 0.32%, which is just below AstraZeneca with 0.42%.

The Johnson&Johnson vaccine has the highest (but still very low) rate with 0.86%.

The order of effectiveness corresponds to the numbers known from other countries.

The full data

Vaccine 
fully vaccinated    
Infections  
percent
BioNTech/Pfizer 248,157 791 0.32
Johnson&Johnson    36,890 316 0.86
AstraZeneca 50,451 212 0.42
Moderna 34,783 62 0.18
       
Total 370,281 1,381 0.37

Source: Ministry of Health - status: 20.09.2021