Colour profiling is a mystery wrapped in an enigma. A quagmire waiting for you as you climb out of the crocodile-infested river…

All those pretty pictures the display offers you are great - but not if the computer doesn't know what the display is set to.

If your display came with a set of profiles, one for each standard, then that would be a start. Set the computer's display profile to the same option as you set the screen to.

If it doesn't, then all you have are half a dozen different ways of not knowing whether the colours are accurate or not.

As it claims to be 'factory calibrated' then they should have given you an individual profile for that calibration, otherwise it was just 'advertising speak', not worth the paper it wasn't printed on.

[...More, after we know what profiles we have to work from…]
. . . probably followed by a brief lecture on hardware calibration. . . ;)

After comments - you'll be best to set it to sRGB full-time. Rec709 is similar to sRGB but designed for video & has a different gamma curve. I don't edit much video, but when I do, I keep my calibration the same. if I play back from my TV, it looks as it should. However, all my hardware, including the TV, is hardware calibrated, so I expect the picture to be the same on all displays in the building.

Set to sRGB basically you have a 'best guess'. As the manufacturer provides no profiles, that's as close as you can get by using presets alone.

If you were to invest in a hardware colorimeter, then you could get closer to accurate, but this is an investment. On Windows, I think the cheap Huey Pro still works [it won't run on Mac any more]. Better would be an X-Rite ColorMunki, or i1 Display Pro or a Spyder 5. The downside is those last two will cost about the same as your display - but it's a buy once, use forever product. All the screens in the house & even iPhones & TVs if you have the right software.