Bandwidth is measured via throughput, not frequency- It is the frequency multiplied by the bus width multiplied by the data rate. So 2560x1440 at 165Hz would require 2560x1440*3*165 Bytes, or 1,824,768,000 or around 1.6 Gigabytes per second. (The 3 comes from 24 bits per pixel). 3440x1440 at 100Hz would be 1.38GB.
However, none of these calculations make sense unless the graphics card is only being used as a framebuffer, which hasn't been particularly relevant, certainly not for games, for a few decades. The System doesn't send full, rendered images to the GPU to be displayed- it gives the Graphics Card instructions and data regarding geometry, shaders, textures, and so on. The GPU's bandwidth affects how quickly it can receive that information from the system. The speed that it can take that data and create rendered output depends on the speed of the Video memory and the GPU, which get's into far more complicated systems than being able to directly compare frequencies.
It will, of course, take more GPU capability to run 2560x1440 at 165fps than it would to run 3440x1440 at 100fps, but that capability is largely centered around the capabilities of the GPU, not the bandwidth of either system or video memory.
Note I don't mention refresh rate. That's a separate consideration as it largely affects when the graphics card can send another display frame. How it affects FPS is going to depend on whether vsync is being used. If it isn't then the GPU is going to throw frames out as fast as it can either way. If it is on, then typically it will end up locking to the highest even divisor. eg if it can only sustain 100fps at 3440x1440 then your actual framerate will drop to 82.5Hz at 165Hz; if 60fps is the best it can muster, then it will be running at 41.25fps. Vsync means that even if a frame is "ready" then the graphics card has to wait until the next VBlank interval before it sends the new frame Sometimes graphics cards can start rendering the next display frame while they wait which can help prevent stuttering- again, this is a very complicated topic and you cannot simply do a few back-of-the envelope calculations to determine what will be sufficient)
