Have you tried re-inserting the M.2 back into the original NVMe slot? It may have just not been seated properly.
Just did the same on my partner's computer 4 days ago and that fixed it. She only had one NVMe slot.
Here's a tip: It is better not to assume the worst. Often the solution is very simple.
To answer your next question:
Yes you are overlooking something. Of course it wouldn't boot in the other machine. You can't just take a Windows ( you don't mention it but I assume you are using Windows) boot drive out of one machine and expect it to boot in another. The set up is according to the hardware, etc. of the original machine.
It just sounds like you have boot problem. Have youb tried repairing it as so:
Use Startup Repair for Windows 11/10 Boot Repair
Windows Automatic Repair is a built-in tool for users to apply and try to fix some normal errors on Windows PC. And you may also try this method to repair Windows 11, 10, 8 or 7 UEFI/EFI boot error:
Boot Up Windows from Installation Media
1. Insert Windows 11/10/8/7 installation USB.
2. Restart PC and boot from the USB stick.
3. Enable Automatic Repair Option.
4. Click "Repair your computer" at the Install now screen.
5. Enable Automatic repair option to fix UEFI error.
6. Click "Troubleshoot" at choosing an option screen > click "Automatic repair".
7. Use Automatic Repair option to fix UEFI boot error.
8. Choose your account from the list to continue Automatic Repair.
When it completes restart your PC, It should boot now.