I didn’t have time to test the rEFInd downgrade yet but found a workaround for the issue with the missing boot entry in the BIOS.

Rebuilding the BCD obviously solves the “problem” (which only HP BIOSes have).

Recovery process in short:

Boot to recovery console Assign drive letter to EFI partition rename old BCD (\EFI\Microsoft\boot\BCD) bcdboot c:\Windows /l en-us /s [Assigned letter]: /f ALL

Still I’m wondering why this is an HP only issue.

Edit: I’m almost sure that “bcdboot C:\Windows /addlast” will also do it but currently do not have a victim to test upon.