How to Use a PCIe 3.0 Card in a PCIe 2.0 Slot - GPU Republic
This compatibility also cuts across the versions of PCIe, so a PCIe 3.0 device can work in a PCIe 2.0 slot and vice versa.
Mainboard Gigabyte -Intel H610- LGA1700(12+13+14th); 2 slot :DDR ...
So, in this case, if you were to install a PCIe 3.0 device on a PCIe 2.0 slot, it would work, but the slot can be a bottleneck.
Can I Use a PCIe 4.0 Graphics Card in a PCIe 3.0 Slot? - TechReviewer
Yes, you can use a PCIe 4.0 card in a PCIe 3.0 slot. PCIe is designed to be backward compatible. However, the card will operate at PCIe 3.0 speeds, not taking full advantage of PCIe 4.0 capabilities.