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The trick is to create a function that access QGIS graphical interface, and that is piped to the query of the select by expression.

1. Open a function editor (from anywhere, including from field calculator) and create a new function that reads the canvas extent and returns it as a geometry.

from qgis.core import *
from qgis.gui import *
from qgis.utils import iface

@qgsfunction(args='auto', group='Custom')
def currentExtent(feature, parent):
    return QgsGeometry.fromRect(iface.mapCanvas().extent())

2. Open the select by expression and use intersects($geometry,currentExtent()) (or within(..) for entirely contained polygons)

The same function can be used in a virtual layer as shown here, that you could eventually modify to compute the buffer.