Now the way I would do it is just call the cop shop and ask them how to take care of it.
Do they speak English? Wouldn't even know who to call honestly...
I wrote an Email to the Polish National Police for the time being.
This system honestly baffles me.
I know now foreigners are usually made to pay on the spot. Instead they told me, I could just transfer the money.
Yet there is no IBAN number to transfer to because, apparently, Polish traffic fines are considered tax and are therefore paid to the tax office.
Which you can only do with a Polish tax number.
The trip alone would cost me as much as the fine and it's not clear, if I can even use the slip at the post office because there's a filed to input that PESEL number again.
I might just never go back again if I cannot resolve this.