Missing results from ReshapeGeometry method on PyQGIS

I am trying to use the method reshapeGeometry from QgsGeometry class in a script to reshape a feature geometry (polygon) according to a line.
The result of the process is 0, so positive, but I can’t see any change in my geometry.

This is an example of my script:

layer = iface.activeLayer()
line = QgsLineString([QgsPoint(1, 1), QgsPoint(2, 2)])

for feat in layer.selectedFeatures():
    c = feat.geometry().reshapeGeometry(line)
    print(c)
    

The feat in this script is a simple polygon with WKT.

Polygon ((1.16531548008501851 1.44378001491727948, 1.60296509683766097 1.93729979551068476, 2.06544589751953112 1.57103983255457269, 1.60296509683766097 1.0309615820938649, 1.16531548008501851 1.44378001491727948))
0

as observable in the image below (in green). The red line is the representation of the line used for the reshaping.

I have tried both to make the layer editable before and saving the edits after and to reload the layer after the operation.

I am working in the PyQGIS console on QGIS 3.16 and 3.19 dev.

layer = iface.activeLayer()
provider = layer.dataProvider()
line = QgsLineString([QgsPoint(1, 1), QgsPoint(2, 2)])

feats_to_update=[]
for feat in layer.selectedFeatures():
    geom = feat.geometry()
    geom.reshapeGeometry(line)
    feats_to_update.append([feat.id(),geom])

provider.changeGeometryValues({
  feats_to_update[0]: feats_to_update[1] for feats_to_update in feats_to_update
})

layer.triggerRepaint()