I don't see how the NAND flavor has anything to do with the interface or protocol specs.
If your laptop says it supports M.2 SSD drives, then it should support SLC, MLC, TLC, etc., drives that conform to the M.2 interface standard.
Are you sure that it didn't say "PCI-E M.2 SSD"? Because there are several different flavors of M.2 sockets, that have nothing to do with the NAND type used on the SSD. Generally, they will be either PCI-E NVMe, or SATA.