I'll have to wait until I can get a change to take the Mini PC apart to take a pic. The old M.2 card has two slots and says SATA C. The Bios is very basic. It only shows what devices you can use to boot from. I went ahead and put the new drive in the Mini PC and tried to install Windows from my flash drive. The drive couldn't be found. I put the old drive back in and tried again. The old drive is seen but shows two partions with a size of 0. I was going to try a 2.5 HDD but I don't have any I can use. I don't know what happened to this Mini PC to cause two drives to mess up. On my USB HDD all of the folders lost the ownership and I couldn't open them. Luckily it was just a matter of taking ownership again. Neither drive shows in File explorer on my desktop using this enclosure I bought.
https://www.amazon.com/dp/B07MNFH1PX?psc=1&ref=ppx_yo2ov_dt_b_product_details
Your drives might not be messed up but, simply not seen .
As I said, you might have to Format the drive and /or
initialise it in Disk Management.
This is why I asked if it is seen on another PC/notebook.
The old M.2 card has two slots and says SATA
That would indicate that it is in fact a SATA drive. The C at the end might just be that it
indicates that it is your "C" drive but, not sure. I haven't seen it named that way else where either.
From what I can ascertain , the new drive is a PCIe Gen 3 drive and Not a SATA drive.
The link you posted for the external adapter is for a SATA drive and for PCIe drive so,
it should work with the new drive. This is why I asked to test it on another device.
From there , you can format if need be.
I have a T7 as storage via a C port and is seen as exFat in Disk management but, it also has a drive letter
assigned to it. When you plug in the new drive in the external enclosure, do you see it in Disk Management ?