In this case, overwriting the web layer is successful. Most likely, the layer IDs assigned in the map changed from when the web layer was originally published, which causes references to the layer to break in the web map. When overwriting layers, it is important to examine layer IDs and ensure they match the existing service. Refer to the following documentation for more information, https://pro.arcgis.com/en/pro-app/latest/help/sharing/overview/assign-layer-ids.htm.