The issue with bank transfers today is that the SEPA system is robust and established, but got no web compatible API.
But there are two projects (why one, if you can have two!?), one being Wero by different banks, the other being the Digital Euro by the European central bank. If either finds good adaption (Wero is rolling out slowly and for quite a bunch of banks every customer already got a Wero account automatically) this could move things around ...
I'm Irish, but I've built a website for an Australian client and they integrated something which did that. In the checkout, you could choose to pay with a system which would log you into your bank's website, where you could approve a payment, then return to the site on which you'd made your purchase, where it would instantly be marked as paid. I think that it may have taken a few days for the money to actually arrive in their bank account, but the payment was authorised instantly.
I believe the usual SEPA flow is either scan this QR code or type this IBAN+reference into your bank's mobile app? SEPA is a "giro" system, meaning the person who owns the money has to push it, rather than a cheque system where the money owner writes something to the merchant who then pulls money from the money owner. These are always less convenient because the money owner has to contact their bank. They're also more secure.