Only if you meet the volume thresholds, which vary by country - e.g. for sales to Ireland you must register and pay VAT if your sales are over EUR 35k / year, but in Germany its 100k.
> At the heart of the 2021 e-commerce EU VAT reboot is the introduction of the One-Stop-Shop (‘OSS’) single EU VAT return and the withdrawal of the Distance Selling thresholds.
[...] Non-EU sellers may also apply to use the OSS regime, and just need to nominate any single EU state to register and file in.
Are you sure this still applies in the case of purely digital sales like SaaS, and for businesses selling into an EU country but based outside rather than domestic businesses selling within their own country?