It turns out that I could update to a more recent BIOS by using the firmware for the DE3815TYKHE which is actually using a DE3815TYKE .
Further, the BIOS was “customized” (it has a specific graphic at startup), and I guess that this customisation prevented updating the BIOS (error 0x8000000000000012 followed by unknown number) - I had to remove the BIOS security jumper so that the BIOS could “recover” to the BIOS file on my USB stick.