OK, found what the issue was.
Restarting the Smart-1 Cloud instance did not fix it.
Install Database on the management server completed without error.
Policy installation failed with the "purged object(s)" error message, even with only either Access Control or Treat Prevention ticked, or with accelerated installation disabled.
(Policy installation task would stay queued in SmartConsole and had to be cleared manually.)
Entering the Updates tool in a SmartConsole policy brought a "Failed to get DB object" error message.
IPS updates status showed a warning sign, with a "loading IPS update statuses" message when hovered on.
IPS database appears to be broken, and manual update went bad (using SmartConsole crashed SmartConsole, update using SMS failed or maybe restarted SMS not sure).
The real fix was just to manually switch the IPS database version (Policy Tools > IPS > drop-down menu > Switch to version).
I guess the management database revision I reverted to was so far away in time (still was just the previous one) that the referenced IPS version had been purged locally, and this broke the IPS state.