Still, my understanding is that if you know the country and classify product like you know the rate. So it is less complex than sales taxes which might be local in other places.
So for EU to EU company it's actually very simple.
But in mean time many other countries made some version of "digital tax". So you want to have this handled by someone anyway.
PL5472244433
This is my European vat number, you can check it on VIES.
Vat is reverse charged from years, nobody pays it in B2B.
B2B sales have VAT applied, but before sending the VAT money it collected, the company deducts the VAT it was charged when it bought the goods. (each company ends up sending tax money that covers how much value it added)
(it's a bit more complicated when it's cross country since it involves refund rather than deducting, but that should be the same idea)