Map extent matching permanently main canvas extent

I think the main issue here is, that there is no option to set the auto-refresh rate of print-layout-maps (at least none that I know of). So you can use data defined override for your extents as below, but the print-layout-canvas will only refresh if you manually click on the refresh button, minimize and remaximize the printlayout window, or something like that. Which makes it a little bit pointless... But in my eyes this would be a nice feature though.

However, you could create a custom function like the following:

@qgsfunction(args='auto', group='Custom')
def my_canvas(feature, parent):    
    e = QgsGeometry.fromWkt(qgis.utils.iface.mapCanvas().extent().asWktPolygon())
    return e

It returns the geometry of your current main-window-map-canvas. You can then use x_max(my_canvas()), x_min(my_canvas()), y_min(my_canvas()), y_max(my_canvas()) as expressions for data defined override for your print-layout-map properties:

PS: I am not an expert in PyQGIS, so I dont know why I had to use .asWktPolygon() as step inbetween. It just failed returning QgsGeometry() directly when using .asPolygon().

Thank you for those first answers. As I have poor knowledge of coding, it'll take time before I meet a result.

My research led me to a plugin (Layout loader) , which is able when opening the composer to zoom directly to the canevas location. However for certain reasons, I am not likely to use that plugin, and so I'll carry on with your solutions.

Here is the link to the plugin : link to Github

And here, an extract of the code:

        # Get current canvas extent and apply that to all maps (items) in layout
    # Replace any text "{{title}}" in any layout label with the dialog Title text
    canvas = iface.mapCanvas()
    for item in l.items():
        if item.type()==65639: # Map
            item.zoomToExtent(canvas.extent())
        if item.type()==65641: # Label
            item.setText(item.text().replace('{{title}}',title_text))