Plug-in to reshape sharp edges to circular string is not working near to start/end point of polygon

Question

I am developing a plug-in in QGIS. By using two points I am creating a circular string to reshape sharp polygon edges to round. The plugin is reshaping 3 edges perfectly but failing reshaping near start/end point of the polygon. Code to execute on right-click given below.

final_vert=[]
if self.layer.selectedFeatureCount() == 1:
   for feat in self.layer.selectedFeatures():
       geom = feat.geometry()
                   
if geom.wkbType() == QgsWkbTypes.MultiPolygon: 
    ver_list=geom.asPolygon()
    close1 = min([geom.closestSegmentWithContext(self.coor[0])])
    idx1 = close1[2]
                    
    close2 = min([geom.closestSegmentWithContext(self.coor[-1])])
    idx2 = close2[2]
    ver_lis = ver_list[0][0]
                 
    if idx1 > idx2:             
       self.poi.reverse()
       geom_part1 = ver_lis[idx1:]
       geom_part2 = ver_lis[:idx2]
       final_vert.append(geom_part2)
       final_vert.append(self.poi)
       final_vert.append(geom_part1)
                        
       pass
  else:
       geom_part1 = ver_lis[:idx1]
       final_vert.append(geom_part1)
       final_vert.append(self.poi)
       geom_part2 = ver_lis[idx2:]
       final_vert.append(geom_part2)
                    
   ab = itertools.chain.from_iterable(final_vert)
   geom_vert = list(ab)                
   blade = QgsGeometry.fromPolygonXY([geom_vert])
   self.layer.changeGeometry(feat.id(), blade)

The code is working well for 3 sides as shown in in the 1st image below. But while reshaping near to start/end point of the polygon it results in removing rest of the portion while keeping the source point at place.

How do I avoid this problem?