Greetings,
Welcome to the forum.
I am not a HP employee.
The M.2 socket protocol is very confusing.
Motherboard manufacturers can implement PCIe, or SATA, or both on the socket.
I would guess your motherboard's M.2 socket cannot support booting to M.2 PCIe devices. The Intel 760p is an M.2 PCIe NVME device.
Windows 10 supports M.2 NVME devices as storage devices even if the motherboard does not support booting to this device.
This is why Windows 10 recognizes the Intel drive as a storage device when you boot to the operating system SATA SSD. Windows 10 installs the correct NVME driver so you can run this drive as a non-bootable storage device.
Your PC may not be able to boot from a M.2 PCIE device.
The BIOS, if it supports booting to an NVME device, should boot to this device without changing any BIOS settings. I have never had to enable NVME drive boot support in any systems I have worked with.
I suspect a M.2 SATA drive will boot correctly.
Regards