I want to merge two partly overlapping raster files which are obviously in the same CRS and have the same cell size, while taking the exact values of one of the input rasters in the overlapping areas, and hence overriding/replacing the values from the other raster in those areas, with QGIS. The problem is that both files have a cell offset of about half a pixel size laterally and vertically.
I tried several tools to merge both rasters (Merge, Mosaic Raster Layers, r.patch) but the output never adopted the exact values from one or even both of the input rasters. I also tried align the rasters with the Align Rasters tool as well as to remove the overlapping area from one of the rasters and then merge the two (now no longer overlapping) rasters, and some operations with the Raster Calculator, but without any success.
Is this kind of operation even possible with input files with an offset and if so, what would be the right way to execute it?