Texture Painting in Blender with Python script

Question

I can Sculpt using Python but am having trouble getting Texture Painting to work.

Here is a working example of Sculpting:

def context_override():
    for window in bpy.context.window_manager.windows:
        screen = window.screen
        for area in screen.areas:
            if area.type == 'VIEW_3D':
                for region in area.regions:
                    if region.type == 'WINDOW':
                        return {'window': window, 'screen': screen, 'area': area, 'region': region, 'scene': bpy.context.scene} 

def sculpt(coordinates, brush = 'DRAW', strength=1):
    bpy.ops.paint.brush_select(sculpt_tool=brush, toggle=False)
    
    brush = bpy.data.brushes["SculptDraw"]
    brush.strength = strength

    bpy.context.tool_settings.sculpt.brush = brush
    bpy.context.tool_settings.unified_paint_settings.unprojected_radius = 0.2
    
    
    strokes = []
    for i, coordinate in enumerate(coordinates):
        stroke = {
            "name": "stroke",
            "mouse": (0,0),
            "mouse_event": (0,0),
            "x_tilt": 0,
            "y_tilt": 0,
            "pen_flip" : False,
            "is_start": True if i==0 else False,
            "location": coordinate,
            "size": 10,
            "pressure": 1,
            "time": float(i)
        }
        strokes.append(stroke)

    bpy.ops.sculpt.brush_stroke(context_override(), stroke=strokes)

points = [(0,0,0)]
bpy.ops.object.mode_set(mode='SCULPT') 
bpy.data.objects['An Object'].select_set(True)
sculpt(points)

This however does not work for Texture Painting:

def context_override():
    for window in bpy.context.window_manager.windows:
        screen = window.screen
        for area in screen.areas:
            if area.type == 'VIEW_3D':
                for region in area.regions:
                    if region.type == 'WINDOW':
                        return {'window': window, 'screen': screen, 'area': area, 'region': region, 'scene': bpy.context.scene} 


def paint(coordinates, brush = 'DRAW', strength=1):
    bpy.ops.paint.brush_select(image_tool=brush, toggle=False)

    brush = bpy.data.brushes["Brush"]
    brush.strength = strength 
    
    bpy.context.tool_settings.image_paint.brush = brush
    bpy.context.tool_settings.unified_paint_settings.size = 100
    
    strokes = []
    for i, coordinate in enumerate(coordinates):
        stroke = {
            "name": "stroke",
            "mouse": (0,0),
            "mouse_event": (0,0),
            "x_tilt": 0,
            "y_tilt": 0,
            "pen_flip" : False,
            "is_start": True if i==0 else False,
            "location": coordinate,
            "size": 10,
            "pressure": 1,
            "time": float(i)
        }
        strokes.append(stroke)

    bpy.ops.paint.image_paint(context_override(), stroke=strokes)
         
points = [(0,0,0)]
bpy.ops.object.mode_set(mode='TEXTURE_PAINT') 
bpy.data.objects['An Object'].select_set(True)
paint(points)

What am I missing?