Forget the animated Ahsoka for a second, this live action Ahsoka MUST and DOES exist on its own. Think about what's presented to the audience about her from the 5 episodes she's been in:
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She was Anakin's padawan
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She left the Jedi order before her training finished
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He became Darth Vader shortly after
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Years later she attempted to train Sabine but failed
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Their relationship was ruined by this experience
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She refused to train Grogu, fearing his attachment to Din Djarin
We first meet her in her own show where she's alone, accompanied only by an ancient droid, retrieving a map that will lead her to a enemy long-forgotten and thought dead by all. She is quiet, reserved, but still very competent. She doesn't want to revisit the past, but is convinced to do so by an old friend.
And Sabine so far:
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Her best friend Ezra, a Jedi, has vanished, thought dead, and she feels responsible to carry on his work
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She failed Jedi training with Ahsoka
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She holds a grudge against Ahsoka for walking away
The relationship between her and Sabine is the heartbeat of the show and the main conflict. Their experience before the events of the show are the unspoken words that drive all the emotional drama. We don't know how that blew up, but we know a little. Due to experience, Ahsoka has difficulty with attachment and training. Sabine has lost someone close to her, someone she'd go to great lengths to save. Maybe their grief manifested in ways that weren't compatible at the time they trained together.
But they need to work together now, to open themselves up to the pain in their past and work through it together to defeat a old threat.
There's a lot of talk about being people being confused by what's happening, or the characters missing their spark from the animated shows, but I think what's been aired so far is a simple but compelling storyline for newcomers, and a thrilling promise for existing fans of these characters that its continuing their journey in a manner that takes their traumatic past experiences seriously while putting them in a position primed to return to their old ways.