Two things. What SSD adapter are you using for the internal installation? From my reading of these forums for years, the Sintech adapter seems to be the most compatible & reliable one. I have rarely seen anyone have issues with it.
Second, was macOS 10.13+ ever previously installed on this laptop? The laptop's firmware must have been updated to the new firmware which usually uses a different format that looks something like 192.0.0.0 instead of the old style which mixed alphabetic characters & numbers. If not, then you must first install macOS 10.13+ while the original Apple SSD is installed internally. Then and only then can you physically install the third party NVMe SSD. You will only be able to use macOS 10.13+ since older versions of macOS don't have the necessary NVMe driver for the new SSD.
If you are booting into Recovery Mode, sometimes a Mac may only boot into the older online macOS installer for the OS which originally shipped with the Mac from the factory which will be too older to work with the third party NVMe SSD.
Another possible issue with macOS 12.x Monterey.....if you did not install Monterey on this laptop while the original Apple OEM SSD is installed internally, then the macOS Monterey installer will refuse to install if the third party SSD is installed internally. Once Monterey has been installed while the original Apple SSD is installed internally, then the laptop's system firmware will already have been updated which means you can install Monterey at any time with the new third party SSD installed internally.
Keep in mind install is a critical keyword here since the laptop's firmware must be properly updated for these two situations when using a third party NVMe SSD internally.