OK I solved my problem.
Now it works! Upgrade succeeded 
Mainboard i7-1280p.
Upgrade from 3.06 to 3.08.
By EFI boot method.
@Benjamin_A_Ewoldt Yes, thank you! Indeed I had to do this kind of steps.
Overall it was not straightforward, so it would need to be fixed in order to go out of beta state.
My steps (I call them “points” to not confuse with the installer’s “steps”):
0 - started the laptop, and the installation process (with F12)
1 - I was stuck, as described in my previous post.
2 - I powered off and waited a bit, and removed the AC and the USB key (I did not need to remove my expansion cards, as they are all 4 just USB-C expansion cards)
3 - I started over again (with F12 key). I needed to try again and reboot several times, because the ports were not ready yet (I should have waited longer). I also used different ports, so that may have helped; maybe some ports were stuck in the middle of the previously failed upgrade.
4 - The process got stuck in the middle because of low battery (although I was at 20%, and I was AC-plugged anyway, but maybe that was due to a faulty or partially-upgraded PD firmware), and the text on the screen advised me to reboot in OS. (EDIT: I forgot to mention that from that point, until my point “6”, there were color codes on the side LED)
5 - I disobeyed the text on the screen and rebooted in the EFI installer again (instead of the OS)
5bis - (actually I think I did the point 5 several times)
6 - the install process just resumed (now I was at step 3/5, etc), seemingly oblivious that the previous step did not happened because of “low battery”
7 - after several scheduled reboots, the text on the screen said that the upgrade was done. I was skeptical, though. So I started again the flashing.
8 - So everything repeated again. But this time there was no battery issue (probably thanks to fully updated/fixed PD firmware). By the way I could check on the info displayed in the screen that the EC version was still 3.06 and being upgraded to 3.08. So I was right to do it again (It stated that the PD firmware was already up-to-date though).
9 - So, after several scheduled reboots, the upgrade was completed. I could check that the BIOS was properly upgraded to 3.08, and everything works correctly for now.
That’s it!
I will report again if I notice problems, e.g. peripherals not working etc.