Drawing a long cursor over a QPlainTextEdit

I'm trying to draw a long cursor in Qt.

I already have a function to edit many lines of a QPlainTextEdit at the same time (<-> alt edition in Notepad++), and my current goal is to display the cursor.

---- old version -------

I wasn't the simplest way, but I planned on drawing the cursor in a QGraphicsScene on top of the QPlainTextEdit (could'nt think of another way). I had a QGraphicsView and Scene transparent on top of my QPlainTextEdit, the QPlainTextEdit is the one that catches the users's events. My current problem was that I didn't manage to scroll the QGraphicsScene.

I know it can work because of this old question : QGraphicsView inside QPlainTextEdit (scrollable widget) but they don't precise how they achieved that...

So at the moment I have my editor (a QPlainTextEdit)

class Editor(QPlainTextEdit):

    def __init__(self):
        super().__init__()

        self.setLineWrapMode(QPlainTextEdit.NoWrap)
        self.setCenterOnScroll(True)
        
        # for the cursor
        self.graphicScene = QGraphicsScene()
        self.graphicScene.addText("Hello world")

        self.view = AltGraphicsView(self.graphicScene, self)
        self.view.show()

        self.horizontalScrollBar().valueChanged.connect(self.view.scrollH)
        self.verticalScrollBar().valueChanged.connect(self.view.scrollV)

and the AltGraphicsView is like this :

class AltGraphicsView(QGraphicsView):
    def __init__(self, scene, parent):
        super().__init__(scene, parent)
        self.parent = parent
        self.setSceneRect(parent.rect())

        # Transparent so that we see the text behind
        transparentBrush = QBrush()
        transparentBrush.setColor(QColor(255, 255, 255, 0))
        self.setBackgroundBrush(transparentBrush)
        self.viewport().setAutoFillBackground(False)

    # Functions to connect the scrolling ... doesn't work
    def scrollV(self, value):
        self.verticalScrollBar().setValue(value)
        self.viewport().scroll(0,-value)
        self.invalidateScene()

    def scrollH(self, value):
        self.horizontalScrollBar().setValue(value)
        self.scrollContentsBy(-value,0)
    
    # Do not catch anything -> "function-transparent"
    def dragEnterEvent(self, event):
        self.parent.dragEnterEvent(event)
        return True
    #...
    def wheelEvent(self, event):
        self.parent.wheelEvent(event)
        return True

When I do not set self.setSceneRect(parent.rect()), the view is the size of Hello world at the top-left of the editor, but the scrolling works (must debug, but works a bit). When I set it, the view has a correct size... but does not scroll with the editor.

I think there's a problem with the size of the QGraphicsScene, but when I tried giving it a larger size than the QGraphicsView with self.graphicScene.setSceneRect(0,0,10000,10000), nothing changed (no scroll).

Does somebody has an idea about how to solve this scrolling problem?

----- new version -----------

Following musicamante's advice, I'm looking into the paintEvent function of QPlainTextEdit. Trying to understand how to draw the cursor so that it remains at the same place when scrolling.