I have a sick feeling that if I had just declined the offered repair and power cycled the Mac Mini, all would have come back ...
Ah well, another lesson learned.
As it is, I had to create a new VM based on haos_ova-10.5.vdi from https://www.home-assistant.io/installation/linux/
This booted successfully, and I hoped I could just login to HA and restore from the backup - but no, because it was a new instance running, it took me through onboarding where you can only create a new user, not login as an existing user.
So everything is gone - fancy dashboards, automations, Apple Watch integrations, usage history - and I am starting from scratch with SpeakToTheGeek on YouTube !
I am DONE with updating HA, and I am DONE with fancy dashboards, Apple Watch integration etc. I will just have a very basic install, just enough to do some Octopus Flux automation, and that will be it. I get that it is a complex piece of software, running on multiple platforms, with multiple maintainers - it is just not stable enough to be used as a single source of truth.
YMMV.
If anyone can point out what I did wrong, how I could have recovered my original setup, please let me know for the next time I feel my finger hovering over the nagging update button ...