linux - Network Interface Card not using the correct PCI link ...
Yes, you can use a Pcie 3.0 graphics card with a Pcie 4.0 slot. Even though Pcie 3.0 and Pcie 4.0 have different data transfer rates, they are cross-compatible.
What is PCIe® Gen 4 for SSDs, and how does it compare to Gen 3 and Gen 5? - Samsung Business Insights
PCIe 4.0 SSDs are twice as fast as PCIe 3.0 SSDs. But next-generation PCIe 5.0 SSDs will double PCIe Gen 4 speeds.
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.
linux - Network Interface Card not using the correct PCI link ...
The different versions of PCI Express are both forward- and backward-compatible with each other, in the sense that you can run a PCIe 4.0 SSD in a PCIe 3.0 slot, for example.