That would mean Adam/He-Man/Adora have reforged that sword as well. To me it is definately NOT the sword of Adora. The stupid new "H" thing on the hilt is very visible and does not resemble the sword of Adora. The snake just has to go towards the viewer at some place to show that a huge number of people is walking on the back of it.
If they are so blind to reshape that sword as well, mostly with not showing how and why, the sword of Adora is unrecognizable and Fans might be angry. At the end of the Adora digital comic the sword looks normal.