The PCIe 4 slot only working with an 11th generation processor probably means that the 10th generation only has 16 PCIe lanes and they all go to the x16 PCIe slot.
The 11th gen processors have 20 lanes and can have a one x16 slot and one x4 slot:
The reason for this is that on most motherboards the first x16 slot is served by the CPU and the remaining slots come off the Platform Controller Hub. On newer processors both the first x16 and first NVMe x4 slot both come off the processor.
The block diagram for your motherboard is going to be nearly identical to this B560 block diagram. Note the CPU serving the "1x16 + 1x4 lanes of PCI Express" in the top left corner.
There is no way for you to use that x4 PCIe 4 slot without getting a processor that has enough lanes for it. That means getting an 11th generation processor. The 10th generation simply does not have those extra 4 lanes of PCIe available.
What you can probably do is get a PCIe to NVMe adaptor like the one below. I have used one of these on a system with an i7-6700 in the past and it worked perfectly.
You may still be limited to PCIe 3.0 though.