Generally PCIe is downwards compatible.
A PCIe x 16 x 16 3.0 would be the same as a PCIe x 16 x 8 4.0 slot.
Just means that the PCIe 3.0 slot would have half the bandwidth speed of a PCIe 4.0 slot.
PCIe x 16 3.0 has a maximum per lane transfer rate of 8GB per second while the PCIe x 16 4.0 has a maximum per lane transfer rate of 16GB as per this tech article: https://computertechnicians.com.au/pcie-4-0-vs-pcie-3-0-whats-the-difference/
What Is The Maximum Bandwidth Of PCIe Gen 3?
The maximum bandwidth of this standard: is 8 Gigatransfers per second (GT/s). This means that 16GB of data can be transferred in less than two seconds
What Is The Maximum Bandwidth Of PCIe Gen 4?
The first thing to note about PCIe 4.0 is that its maximum data rate has been doubled compared to PCIe 3.0 – from 8 GT/s to 16 GT/s. This means that each lane can transmit up to 16 Giga transfers per second in both directions simultaneously.
Now the issue I might see is if your GPU card can operate in a PCIe x 16 3.0 slot or it is engineered to work only on a PCIe 4.0 slot.
I have read that some Users, here at AMD Forums, needed to set in BIOS the GPU Slot from 3.0 to 4.0 for the latest AMD GPU cards to work correctly or even work.
My Personal opinion would be the card should work in a PCIe 3.0 x 16 slot without issue just possibly in certain circumstance not as fast and certain GPU features may not work or work as well.
Either way I would open a AMD SUPPORT Ticket - https://www.amd.com/en/forms/contact-us/support.html and ask them directly if that GPU card is compatible to work in a PCIe 3.0 slot or not.
