How to sum pixels of two overlapping rasters with different extents

I have two DEM rasters which overlap and have different extents. I would like to create a new raster which sums the pixels where there is an overlap.

I tried using gdal_calc first by doing A+B but seeing the rasters are different dimensions it errors.

I then tried using gdalwarp using the -r sum. This creates a raster but it has not preformed a sum.

I have successfully performed this in QGIS using the raster calculator, but as I will eventually be running it on multiple files I’m trying to get a command line solution to work.

The closest solution I’ve found on Stack Exchange is this question Using rasters with different dimensions in GDAL_calc.py

Is there another way?