That's still Dial-up.

56k was just the last version of Dial-up. I started on 9600baud (9.6k) and it started well before that even, at something like 0.1k.

In my experience almost anyone referring to dialup is talking about 56.6k, or at the very least some sort of modem connected to the PTSN, screeching noises and all. Is your experience different?

You had the internet through a mobile phone and you're calling dial up lucky? Mobile phones were legit space age back then.