Umm…
I just accidentally reloaded the ACF-Upgrade page whilst it was still loading.
It immediately refreshed to the “compete” page:
Advanced Custom Fields Database Upgrade
Reading upgrade tasks…
Upgrading data to version 5.3.9.2
Database Upgrade complete. See what’s new.
This rather suggests the operation was complete hours ago.
Unfortunately, I only discovered this by accident, four hours after I clicked “upgrade”.
Something obviously went a bit wrong. Don’t know if it was due to the size of my database or what.