TL;DR:
I found an xhci_hcd error linked to an incompatible SSD enclosure, I switched to a better SATA to USB and retried. Initially encountering a supervisor error, a reboot resolved it, and the system was successfully up and running 14 minutes after starting the process.
Hello @e-raser & @FloatingBoater
Thanks for your replies. My original data disk was 27GB of my 32GB SD card.
After leaving the system for 5+ hours I finally decided it was time to pull the plug. I connected a monitor to my raspberry pi and rebooted it. The system was unable to start and I eventually had to restore from a backup. But(!) using the monitor showed several errors, the most relevant was an xhci_hcd error which lead me down a path to discovering that my decision to save a few dollars on an SSD enclosure was not worth it. Apparently this does not play nice with RP4. So, I bought this and tried again this morning. With the monitor still connected I initiated the data transfer, this time the HA text said about 10 minutes. I stayed close, watching the monitor, and in less than 10 minutes the system was starting, things were looking promising! There was one small hiccup, I saw something about a supervisor error on setup and couldn’t connect to the system (on port 8123), but I was able to connect to the HA observer (on port 4357, something new I learnt during all this) so I decided a reboot might work and pulled the plug.
Then, in a few minutes, now 14 minutes after starting the move data disk, my system was up and running!