This is an apples-to-apples, Hungarians-to-Hungarians, same time period comparison! Pretty much the only variable is the extent to which those counties vaccinated their citizens by July 2021, including young people likely to make babies. Again, to remind you: the vaccination rates are a snapshot for July 13, 2021. You can add 9 months to July 2021, which gives you April 2022. Thus, you can see why birth rates in Q1 2022 changed: because of Covid vaccination.
The result? The more vaccination, the greater the declines in the birth rates.