I'm working with the OSM layer (black and white). I would like to create a buffer in which the OSM layer will become colored.
Is there any option to combine 2 different OSM layers at the same map?
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I'm using QGIS 3.10 but I believe this works for 3.4 as well. Zoom until you have the buffer area in your view then go to Project>Import/Export>Export Map to Image. In the resulting dialog click on Map Canvas Extent to set the extent of your export to what you see on the screen. Also make sure that the Append Georeference Information is checked this will enable you to bring the image back into QGIS and have it show up in the right place. This will either be embedded in the file or as a separate file with the same name. Press save and save it in the format and place you want. After it has been saved bring it back into QGIS treat it like any other georeferenced image file. In this case clip it with your buffer and turn on grayscale. Here is a related thread How to clip an Openlayers OSM Background to a Vector Boundary?
Alternatively you could use a transparency blending mode on your buffer to get a similar effect. See this thread for some ideas. https://www.reddit.com/r/QGIS/comments/c8wq78/how_can_i_recreate_this_grayscale_mask_effect/