I used to work at an research/architecture (buildings, not software) firm that was a leader in carbon emission estimation. To estimate the carbon emissions from building operational energy, what we did was find the rate of carbon emission at the local grid[1] and then multiply it by the predicted operational energy from an energy model. For example, for a single family home drawing from a blended grid mix of coal, gas, and nuclear, you might have a carbon emission rate of 150 kgC02/MBtu for 0.04 kBtu/ft2 of operational energy, over the course of an hour. This works out to:
150 kgC02/MBtu * 4E-5 MBtu/ft2 = 0.006 kgC02/ft2
You then integrate this over the course of the year. This gets complicated as there are variations in the resolution of carbon emissions from different grids, the grid emission rates, and which grid the building uses.
To estimate server carbon emission rate, you just have to swap the building energy use intensity for server energy use, and everything else should be the same.
[1] Grid Emission Rate Sources
EPA: https://www.epa.gov/egrid/data-explorer
WattTime: https://www.watttime.org/