You need a SATA M.2 SSD. The NVMe SSD are not compatible. Laptopmedia here has more on the specs of the 9343.
Dell XPS 9343 with latest BIOS 9343_A20 The original SSD died (I surmise as I have not tested it elsewhere) so I bought a replacement SSD.  The BIOS will not detect the new SSD no matter what settings I use. - Legacy or UEFI. I have updated the BIOS using Dell flash BIOS USB method. I created a win10 recovery USB and when installing Windows using this method windows will find the SSD, but when the laptop reboots, I remove the USB, and it will be 'file system not found', or if the USB is left in place it will be back to the start of the win10 install. So I suppose the root problem is the BIOS will not recognize the new SSD. I have tried this with 2 different SSds with the same result. First of all a Samsung 970 EVO Plus MZ-V7S500BW | Internal NVMe M.2 SSD, 500 GB then a Kingston NV2 NVMe PCIe 4.0 SSD 250G M.2 2280 - SNV2S/250G                  
New SSD not found in BIOS, but found in Win10 recovery USB