In order to use the adapter you purchased for m.2 your motherboard not only needs to support SATA (which this does) through the m.2 slot, it also needs to support SATA PM (port multiplier). This is a separate standard than just plain SATA. I suspect your board does not. Or if it does, it needs to be enabled in the BIOS.
The other option you can use here is to put a SATA expansion card in one of your two PCIe slots. But perhaps you already have something in those. In which case, the only other option at that point would be to start connecting via USB instead. You can do this internally via an adapter, but you are limited to the speed of whatever USB connector you’re tapping into. Same applies for external.
Otherwise you’ll need a motherboard with more SATA support, or SATA PM.