How can I get my 13" MacBook Pro to detect the NVMe m.2 drive that I installed?

Make sure in disk utility you have shown all disks/drives/volumes and not just volumes as is the default view.... A bare unformatted drive is usually not shown especially in High Sierra+ where they introduced APFS because of the new file structure. Click on the gear or down arrow and show all devices in the left side are of disk utility and see if you can then see the nvme, click on the very root of the drive not a volume and format it to apfs. If you don't see it to do this, then you have a bad adapter probably and should buy the one that's most recommended. Nvme support isn't as great as I'd hoped on my 2014 MBP either. I fixed the slow to restart and sleep issue but the system still doesn't recognize it at boot for almost 20 seconds (even after selecting it as the startup disk as many have suggested, that didn't help a thing for me) it simply takes several seconds to see it unless I boot and hold option key and then select it which is much faster to show it but still a pain to have to do. I actually pulled mine and use it in my m. 2 slot on my Windows Z390 Mobo instead as I restart and or sleep the Mac alot in my work (I'm in and out of car a lot) so it really wasn't practical for me. But try showing all devices in the left pane.... It should be there if you don't have a bad adapter.

the attached is what you want to see in order to do the proper formatting etc.

you will need to set it up with high Sierra 10.13.6 and it will recognize it