That problem won’t fix. The OSM-monochrome style was provided by a third party (wikimedia labs) that won’t continue the service.
So you will have to use another style (background map) in the future. Stamen toner or Carto positron might be feasible, but the data may be outdated. See https://wiki.openstreetmap.org/Tile_servers for more options but please note that all wmflabs tile servers won’t work anymore as of now.
A much easier approach is to use the standard OSM-Carto & select a symbology which renders it in greyscale (I think I use equal luminance). I often do this when using a coloured base map clashes with the information I am presenting.
Thanks SK53, you gave me a good suggestion!
In the OSM wms (standard) Layer property I’ve reset the Saturation, adjusted the Grayscale and Contrast parameters and the background has become so very similar to the original Monochorme OSM.