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/Pfizer248,1577910.32
Johnson&Johnson   36,8903160.86
AstraZeneca50,4512120.42
Moderna34,783620.18
    
Total370,2811,3810.37

Source: Ministry of Health - status: 20.09.2021