Some of these issues are motherboard dependent - some have different names for their settings and some have more settings than others. My board is two generations newer than yours and it worked pretty easily. Here's a thread with some ideas to check out. Most points may not apply, but maybe your fix is buried in there.
m2 SSD not detectable in BIOS | TechPowerUp Forums
Couple other things to check are:
- When you boot from your original win7 boot drive...
..... does the nvme drive show up as pci-e, or just sata attached. An m.2 nvme drive can run either way and you obviously want it to be pci-e.
.... Try replacing the microsoft nvme driver with the manufacturer's driver for your nvme. Mine is samsung, I do not use the windows nvme, but some nvme manufacturers do not have their own driver so you have to stick with microsoft.
..... are both drives the same partition type (both MBR or both GPT)
- The instant you finish a clone you need to shutdown and remove the original drive because if you boot again from the original drive, the boot sector of your nvme drive gets altered and may become unbootable. This means when you do things like I suggested above (e.g. check on sata vs pci-e mode with the nvme as the non-boot drive), you will need to re-clone afterward. Alternatively, you could use bootsec or other tool to repair the boot sector but I wont go into that. Easier to just re-clone.
- You mentioned the nvme does not appear on the bios boot menu but if it does not even appear in bios that's another story. The bios itself does not require a valid boot sector in order to detect a drive but the bios boot menu does require a boot sector. So next time you boot from the nvme look in bios to see if it detects the nvme (hopefully as pci-e, not as sata - check both places). If so set it as the boot drive within bios itself, then save the bios settings. Avoiding using the bios boot menu for now.