It can start making that noise anytime in it's life of service. Drivers are a coincidence. Put the old ones back in, it'll still make the sound. You can't argue electronic facts because they're like laws of physics. I'd say 98% of video cards develop a whine or hiss in their lifetimes. Some brands are worse than others. My 7 month old Gigabyte RX 5600 XT just started buzzing every now and then, mainly on boot. No performance loss, heard way worse. Every card I've ever had has made coil whine at some point.
Do what @colesdav says and run a frame limiter or set one in the game if it has it. Run lower texture resolution, see if anything makes it better or not. Either way, I and any electronic engineer guarantee the driver didn't cause a hardware noise.
RMA the card and the next one will do it too at some point. Change brands, it'll do it at some point. Nvidia's do it too. There is no escape but running onboard CPU graphics like an AMD A-10 or the 3200G, or Intel's 630 HD graphics built in. Then the onboard audio will act up, it never ends.
If something is electronic and uses any circuit with a device that reduces or increases voltage/current, there's a possibility of audible noise. That goes for PSU's, CPU's, onboard audio, northbridge (older boards), monitors, etc., etc.
"It worked before you broke it!"
