It’s so normal that I can’t actually remember it ever being any different. Even before the advent of mobile banking it was the same with internet banking. Instant transfers.

In the US we have Zelle which is free and instant, but it's still a third party your bank integrates

In Australia we've had free next business day transfers for as long as I can remember. Decades.

The transition to transfers that clear in seconds was happened gradually as bottlenecks were removed from the infrastructure one by one. Some transactions were instant a couple decades ago, but it's only in the last few years that most transactions are instant here.

These days, Visa/Mastercard are basically the slowest way you can pay someone. It's still the most commonly used option though, since it has the best fraud protection.

I do this in the States. Maybe you haven't noticed the option on the bank's site? Also make sure to use a credit union.