I have two overlapping SHPs. One is with two noncontinous polygons - values 0 is blue and 1 is green. Now I have 9 meters grid for the same area, but I need to "fill" the grid with values from previsous shapefile - not by averaged, but by maximum value (it means when one small polygon with value 1 is underlaying the grid, then the whole grid cell has new value 1). Below is the picture. I'm afraid all this spatial join tools does it only by averaged values.
Look at the answer here: How to get the "Join attributes by location" features on a QGIS Mac version . Use the Join by Location (Summary) tool . you can find it in the Processing Toolbox.