Same here. I've got accounts at two different banks, and when I transfer money from one to the other, it's usually there literally the moment I approve the transaction. Within a second. I don't know if it's just as smooth across (internal EU) borders, but I don't see why it wouldn't be.
It's possible that it does require both banks to have implemented these instant payments. Both side have the ability to delay the transfer, but it's possible that these days they're required to support instant transactions.
My experience of sending money from Czech republic (in EU, but not in Eurozone) to a bank in Netherlands via SEPA is ~4-6hours during banking hours, but I was surprised by immediate transfer from Slovakia (in EU and in Eurozone) to the same account.
IIUC, banks can choose which other banks to interface with, provided that both banks are connected to the same clearinghouse. For example, I think some Netherlands banks still choose to limit instant payments only to other NL banks.
It's possible that it does require both banks to have implemented these instant payments. Both side have the ability to delay the transfer, but it's possible that these days they're required to support instant transactions.