Getting the screen position (in pixels) of feature in Print Layout with PyQGIS

Question

I have a PyQGIS script that I'm using to generate a series of maps. These maps are individual frames that will be put together in a video. I would like to add some fancy animations associated with a particular point on the map using video editing software, but to do so, I need to extract the position (in print coordinates/pixels) of a point on the map.

How do I do so?

def print_map():
    # create a print layout
    layout = QgsPrintLayout(project)
    layout.initializeDefaults()
    layout.pageCollection().page(0).setPageSize(QgsLayoutSize(size.width(), size.height(), QgsUnitTypes.LayoutPixels))

    # put the map on the layout at the specific position and scale
    map = QgsLayoutItemMap(layout)
    map.setCrs(QgsCoordinateReferenceSystem(4326))
    layout.addLayoutItem(map)
    map.setRect(20, 20, 20, 20) # I don't know what this does, but it is required
    map.attemptMove(QgsLayoutPoint(0, 0, QgsUnitTypes.LayoutPixels))
    map.attemptResize(QgsLayoutSize(size.width(), size.height(), QgsUnitTypes.LayoutPixels))
    map.setExtent(QgsRectangle.fromCenterAndSize(fancy_math(), more_fancy_math(), even_more_fancy_math()))

    # I'm looking for a function that does this; target_point is a QgsPointXY in map coordinates and position_on_image should be the number of pixels from the top and left of the exported image
    position_on_image = map.getPositionOnImage(target_point)
    # export the position for further processing with a video editing program
    write_to_csv(position_on_image)

    # export the layout too, which also gets loaded into the video editing program
    exporter = QgsLayoutExporter(layout)
    settings = QgsLayoutExporter.ImageExportSettings()
    exporter.exportToImage(filename, settings)

Note: I found QgsLayoutItemMap.mapToItemCoords(), but it doesn't seem to do what I want (the produced coordinates are not right, and I don't know what it is doing).

EDIT: Using the QTransform map_layout.layoutToMapCoordsTransform().inverted()[0] produced a value, which when multiplied by exactly 11.8110236221, gave me the correct position in pixels. I don't know what that magic number represents.