This Omni short story was from the late 70s or early 80s.
Borovsky's Hollow Woman by Jeff Duntemann and Nancy Kress was published in Omni in October 1983.
The story is about a construction worker, Mikhail Borovsky, who is working in Low Earth Orbit, and his relationship with his artificially intelligent suit, who is called Laura.
Construction workers wear boots with magnets in them to keep them from floating away in zero gravity.
An early paragraph states:
Laura adjusted the magnetism in her boot soles. Just enough to add a little friction, a little sureness. If she fell outward from the rotating structure into the starry darkness the steelworkers called the Pit, no one would fall after to her rescue.
Furthermore, you write:
A man obtains an advanced edition space suit with a personality and a "soul".
The headline on the first page of the story reads: "Laura's soul belonged to a man who demanded utter loyalty, no matter what the cost," clearly implying the suit has a soul.
The story is about the pros & cons he encounters.
The story begins with Laura going in search of and finding Borovsky, who has been injured in a fight. However, it soon turns out that despite having saved him, he's not entirely happy with her.