Where does Cinnamon find available desktop themes

While setting up a backup PC last week, I discovered problems with Cinnamon theme settings, especially the main theme.
Both PCs are using Ubuntu 20.04.4 LTS, and Cinnamon 4.4.8 as the Desktop environment.

On my main PC, Cinnamon was originally set up from a PPA, and it has continued working fine since Ubuntu adopted it into its own repository, with Day-of-Ubuntu wallpaper, and the old 'Human' theme.

In System Settings / Themes, I find:
Window borders show as 'Human', but with a blank image; and if I click on the button to show alternatives, I get only what looks like a wide slider bar, but which must be a totally blank display window.
Icons show as 'gnome', with a folder-image; showing alternatives gives a fairly full list, apparently reflecting /usr/share/themes.
Controls show as 'Radiance', with another blank image, and for alternatives I get a fairly full list, again seeming to reflect /usr/share/themes, but with blank images against most of the entries, except for Adwaita, Adwaita-dark, and HighContrast, which show the expected widgets.
Mouse Pointer shows Adwaita, with a cursor image, with alternatives given as DMZ-White, DMZ-Black, Handhelds, redglass, whiteglass, and Yaru. The last four all show an unlikely stock image; and Adwaita does not appear.
And finally, Desktop is shown as Cinnamon, with that as the only 'alternative'.

Cinnamon --version gives:
Cinnamon 4.4.8

Screenfetch gives:
 OS: Ubuntu 20.04 focal
 Kernel: x86_64 Linux 5.4.0-105-generic
 ...
 DE: GNOME 3.36.5
 WM: Muffin
 WM Theme: cinnamon (Human)
 GTK Theme: Radiance [GTK2/3]
 Icon Theme: ubuntu-mono-light

I'm aware that the 'Human' theme, still in the 20.04 main repository, is stuck at GTK2; I have installed the more recent replacement human-theme-gtk from PPA, and gnome-tweaks was happy to accept that as the Applications theme; but it didn't persist, and gnome-tweaks now shows
Applications: Radiance, Cursor: DMZ-white, Icons: Ubuntu-mono-light

On the backup PC, ubuntu 20.04 LTS was set up as a totally fresh install, and Cinnamon set up from Synaptic, with the same version as on the main PC. A complete copy of my home directory was rsync'd to the backup.
In System Settings / Themes, I have reasonable images showing against all current settings.
:Window borders show as 'Bluementa', (probably my selection, since 'Human' wasn't showing; I think it simply had 'Default' and a blank image; if I click on the button to show alternatives, I get BlackMATE, BlueMenta, GreenLaguna, and Menta - all with decent images.
Icons is much as on my main PC.
Controls shows Adwaita, and alternatives show a much wider choice, though about one-third of them show only blank images. This list does not include the old 'Human' theme, but does include the four colour variants from human-theme-gtk, also installed on this PC from PPA.
Mouse Pointer shows Adwaita, with a cursor image, with alternatives given as before, but with the addition of mate and mate-black (both of these with that strange and unlikely stock image, also shown again for Handhelds, redglass, whiteglass, and Yaru .
Desktop is shown as Cinnamon; but here there are alternatives - BlackMATE, Blue-Submarine, BlueMenta, Green-Submarine, and Menta.

So Cinnamon 4.4.8 shows some awareness of /usr/share/themes, but does not conform to those theme entries as Gnome-tweaks appears to do.
Installing Cinnamon 4.8.6 from PPA might resolve things; but before I do that, I'd like to work out why the current version isn't playing ball properly.
Does anyone know where Cinnamon 4.4.8 is looking for the available themes???
Even better, does anyone know how Cinnamon 4.4.8 can be taught to behave better?
Or has anyone installed 4.8.6 and found that previous problems have been resolved?

**I tried posting this to AskUbuntu, but that appears to be stuck at 'Step 2: Review your question. Loading ...' **