My monitor doesn't show its native resolution of 2560x1080 on my Mac
Your Mac has limits in the resolutions it can send to the monitor and the monitor has limits in the resolutions it can show from the Mac.
The monitor communicate with the Mac and sends it a list of predefined resolutions it wants to get. The Mac does or doesn’t activate each of these resolutions depending on its own capabilities.
For example, the monitor will send 1920x1080 at 60Hz as well as 2560x1080 at 60Hz as its wanted resolutions.
If 2560x1080 at 60Hz doesn’t fit the Mac’s capabilities, then the Mac will only activate 1920x1080 at 60Hz.
In this case, there's no other predefined resolution claimed by the monitor that fits inside the Mac's limits.
SwitchResX doesn't push these limits. SwitchResX helps creating resolutions within the Mac's limits.
With SwitchResX, you could define new resolutions that fit inside the monitors and the Mac’s limits, but that are not natively claimed by the monitor.
Please note that defining 2560x1080 at 60Hz in SwitchResX is of no use: the Mac does already know that the monitor wants this resolution, but the Mac has refused to enable it. Defining it a second time will be useless: the Mac will refuse it again.
However, you can define 2560x1080 at 40Hz, which is a resolution that the monitor probably could handle.
SwitchResX will help the Mac and the monitor into finding a resolution that matches their capabilities and is better than the only 1920x1080 resolution that you now have.
For this, you only have to define a custom resolution in SwitchResX with the parameters of the native resolution of the monitor (which you can get from the monitor’s EDID), and lower the frequency before saving the resolution (to 40Hz, for example). Then save the settings and reboot when SwitchResX asks it.
After reboot, the resolution should be available. If selecting the resolution does work, you can try again with a slightly higher frequency (45Hz, etc) until you face a limit.
If however selecting the resolution brings a message on the monitor like « out of range » then you’re out of luck: that means the monitor doesn’t like the lower frequency resolution, and that there's no resolution that fits in both your Mac and your monitor's limits and theses limits have no common space. This cannot be corrected by any software, in this case.