Thank you very much jock,
I still don't have all needed knowledge, but I am lucky to have the H5 working, so before reading your answer I tried two script that are in my H5 and not in the H3 image, such as /etc/default/ap6212 and /etc/init.d/ap6212-bluetooth. Especially the last is invoking, among the other things, just the hciattach you were mentioning, and also devmem2* and rfkill that were missing in the h3 environment (very strange the rfkill missing!)
Now, invoking ap6212-bluetooth by hand, I finally had the bluetooth working, but wifi stopped working and I had to relaunch it via armbian-config (deactivate/reactivate with my wifi ESSID).
Now the last missing piece of the puzzle is: who and when should launch /etc/init.d/ap6212-bluetooth at startup, especially in order not to mess up bluetooth and wifi?**
I'm continuing to investigate, anyway thanks a lot for the very useful overview
*: I took it from here https://github.com/henla464/WiRoc-StartupScripts/blob/master/devmem2 , thanks to Henrik Larsson
**: UPDATE: I found how it works and used
sudo update-rc.d ap6212-bluetooth defaults
that makes the correct links for the boot execution levels described in the script header.
Now everything works, bluetooth+wifi.
Thank you for having triggered the right path of searching!
ap6212
ap6212-bluetooth