34gn850 is amazing monitor, but definitely pricey. put a lot of hours on mine, tbh only downsides are black levels aren't that great and no swivel. i think there's a newer model that's a bit cheaper, forgot the model name.
3080 or 6800 xt are great gpu for 3440x1440 144hz+. you won't get high fps in every game, but doable and g-sync compatibility helps a ton
tons of modern games support 21:9. if a game doesn't it's usually a simple ini fix or something. pcgamingwiki or wsgf are great resources. and seeing that you have 3080 it's a great pair. but bear in mind that still won't reach high fps in intensive games like cyberpunk or with raytracing enabled even with DLSS. least that monitor is g-sync compatible so it'll smooth things out when fps fluctuates. another thing too is fov, some games don't let you change it very much or causes fish-eye effect, and on ultrawide adjusting fov is a must
So I was fortunate enough to secure a 3080, but feels like the temperatures are too high. was playing cyberpunk and temperatures rose as high as 85c, and clocks fell below boost. this was with stock everything, including fan. tried ac valhalla and rose to around 82c. don't think it is my case in particular because it ran my 2070s just fine. tried to crank the fan speed and it helped a bit, but now it sounds like a jet engine.. evga 3080 xc3 btw
actually depends on the monitor. if it's one that has freesync premium (pro) and a wide range, it should support LFC which can enable adaptive sync below the minimum by doubling the refresh rate. but i'd still stay above the minimum, the LFC is best when you get stutters
3440x1440 benchmarks if anyone's interested: https://www.pcgameshardware.de/Geforce-RTX-3080-Grafikkarte-276730/Tests/Test-Review-Founders-Edition-1357408/4/
it's in german but you can filter out the results. for me tho, seems very good at this resolution, tho i am curious about 3840x1600 benchmarks
gsync has a dedicated proprietary module inside the monitor, gsync compatible doesn't have it and is usually freesync, but is tested and verified by NVIDIA. the former has a range of 1hz to the max refresh rate, variable overdrive, sometimes ULMB, etc.
Works out of the box for me. in fact it's already enabled when i plugged it in. 48-144hz, but seems LFC is supported so you could say 1-144hz. its a great panel too, very good colors, very fast, some IPS glow
it can do 160hz as well but is 8-bit color
but if you want cheaper i heard of the Acer nitro XV340CK