I know that back when dial-up internet was a thing the max theoretical speed of a connection was 56kbit/s, but I was wondering if now with modern tech it would be possible to transfer data over this speed. What would be the limit in this case?
The answer is still the same* -- a dial-up service works over POTS, plain old telephone system, and is limited fundamentally by the bandwidth of the voice signal, which is around 4kHz. After the last mile, the analog phone signal is either fully digitalised (at 8bits, 8kHz) or low pass filtered and modulated to a higher frequency in order to allow several calls to be transmitted simultaneously at the same wire.
A fully digitalised ISDN was compatible with POTS allowing a full 64kbps (see the magic numbers above) over a single connections and 128kbps over two lines.
The twisted copper wire ending in a socket at your home can be also repurposed using ADSL(2, 2+) modulation techniques allowing theoretical 8 and 24 Mbps downstream connections and 1-4 Mbps upstream connections -- but this means also that the service provider needs to add their modems at the service utility boxes, which may or may not be compatible with the POTS.
*assuming there is a POTS service anymore available. At my neighbourhood copper was removed probably 10 years ago due to the drop of subscribers (in the process also the possibility to use ADSL was lost...)