A PyQGIS solution:

##### The layer tree  
It contains the 'simple fill' (or background) layer, the layer with the overlaying symbol, and a third layer (duplicate of 'simple fill' layer) which will receive the merged symbol - this layer should have Single Symbol symbology to start.

[![enter image description here][1]][1]

##### The script
```python
# the current project
p = QgsProject.instance()

# the layer with the simple fill symbology - change the name according to your project
lyr1 = p.mapLayersByName('polygons (simple fill)')[0]

# the layer with the overlaying symbology - change the name according to your project
lyr2 = p.mapLayersByName('polygons (overlay)')[0]

# a duplicate of either lyr1 or lyr2 (set to single symbol) - will receive the merged symbology - change the name according to your project
lyr3 = p.mapLayersByName('polygons (target symbol)')[0]

# get the renderer to merge
source_renderer = lyr2.renderer()

# clone the renderer from 'simple fill' layer ready to accept merged symbol
target_renderer = lyr1.renderer().clone()

# get categories of source and target renderers
cats_source = source_renderer.categories()
cats_target = target_renderer.categories()

# loop through categories and merge symbols
for i,cat in enumerate(cats_target):
    # the symbol of the source layer
    sym_source = cats_source[i].symbol()
    
    # the symbol of the target layer
    sym_target = cats_target[i].symbol()
    
    # append the symbol layer from source to target
    sym_target.appendSymbolLayer(sym_source.symbolLayers()[0])
    
    # update the category's symbol
    target_renderer.updateCategorySymbol(i, sym_target)

# apply the merged renderer to the target layer
lyr3.setRenderer(target_renderer)

# propogate changes to QGIS GUI
lyr3.triggerRepaint()
lyr3.emitStyleChanged()
```

##### Result

[![enter image description here][2]][2]

##### Warning  
Run the script only once. Running it again will crash QGIS due to mismatches between the original and new symbols.

  [1]: https://i.sstatic.net/mFMNA.png
  [2]: https://i.sstatic.net/DyGOs.png