A PCIe interface is made up from one or more "lanes". Each lane is made up of a pair (one in each direction) of high speed serial transceivers. More lanes give you more bandwidth.
Some but not all PCIe interfaces support "bifurcation". The same transceivers can be used either to support a single large link, or multiple smaller links. At least some ICs that support bifurcation require the bifurcation to be configured explicitly and the implementers of boards with those ICs on may or may not expose said configuration to the user.
There are two ways to design a PCIe x16 to 4x PCIe M.2 Card*. The cheap way is to just bifurcate the lanes coming from the host. The problem is this only works in some systems, the slot must have all 16 lanes connected, the hardware driving the slot must support bifurcation and the firmware must allow the user to enable that bifurcation. If bifurcation is not supported or enabled then you will only see the M.2 device that is connected to the first four lanes.
That appears to be the situation you are in. You have a bifurcation based card, but either your motherboard doesn't support bifurcation, or you have not managed to find the option to enable it (unfortunately motherboard manufacturers are not consistent in their terminology for this stuff).
The other way to design such a card is to include a bridge chip on the card. The bridge chip presents a proper x16 interface to the host and four separate x4 interfaces to the downstream devices. No special configuration is needed on the host computer, and the card can still operate if the upstream interface is narrower than the full x16.
The problem is that bridge chips big enough for the job (32 lanes total, 16 upstream to the host and 4x4 downstream to the SSDs) are expensive and the cards aren't exactly massive sellers with huge economies of scale. The end result is that bridge-based cards are rare and quite expensive. On a quick search the only vendor I could turn up was "sonnet" (a manufacturer of professional AV gear) with their cards costing hundreds of pounds. I'm sure I've seen others in the past but I can't turn them up right now.
It's usually fairly easy to tell the difference between the two visually. A bifurcation based card will have tracks running directly from the m.2 slots to the PCIe edge connector and will generally only have relatively small ICs. On a bridge based card the tracks from the edge connector and M.2 slots will instead run to a large bridge IC.
* To further confuse matters there also exist PCIe cards that are designed for SATA M.2 drives. You can usually identify these as they tend to be x1 cards and they tend to have B key rather than M key slots.
