So... the timeline is definitely off. In the ET movie the Star Wars Trilogy about Luke Skywalker and the fall of the empire had already begun to be told here on Earth (Return of the Jedi was released the following year), that's how Elliot has toys depicting Yoda and Boba Fett. So the events of ET must take place at least after the events of episodes 4 and 5. With this in mind, it may be more likely that in the days of the fallen republic, and first years of the Empire the Asogian on the ship(s) that visited Earth, wishing to distance themselves from the Empire, began exploration outside the bounds of their galaxy, and came ultimately to ours.
Being still in contact with the Asogian that remained in the bounds of the Galactic Empire, the visitors to Earth were able to tell the story to George Lucas, who then put them to film. Intergalactic communication being somewhat limited, however, means that the visitors to Earth were getting delayed messages, hence the story taking place "A long time ago in a galaxy far far away..."
With this explanation, ET, as a character, may well have been an untrained Force sensitive Asogian. Since he and his ship were so far away from anyone that could have possibly trained him in the ways of the Jedi or the Sith. His abilities were quite useful on the science vessel, so he did practice them, and as we see with the abilities of Grogu in the "Mandalorian" series, they have a tendency to exhaust him.
ET's connection with Elliot was also a Force ability, and it is possible (even likely) that Elliot was a weak Force sensitive as well, but since he probably had no knowledge of his abilities and no one to foster or encourage them here on Earth, his abilities faded (again, as indicated is possible in canon by Ahsoka Tano in the "Mandalorian" series).
ET didn't "give life" or "create life", but he did tie his life force to that of Elliot, an ability that seems to be in line with what can be done with the Force, but in this case you shouldn't think of Force abilities as "Jedi" or "Sith" abilities, the Force is just the Force, since ET was untrained and not associated with either Jedi or Sith.
The Force isn't "light or dark" or "good and evil", it is balanced, but the orders of beings that can use the Force have divided up many of the powers and abilities that the Force is capable of augmenting and manifesting based on their moral codes. The Jedi and Sith are therefore just codes that are in place by some of the life forms that can use the Force. (For example: moving things is not unique to Jedi or Sith, it just is, and both Jedi and Sith use it without naming it a "power from the XX side of the Force" and the same goes for many other Force abilities).