A natural journey for Ahsoka from here on out would be coming back from this state of mind, and letting go of her past experiences (actually, we saw this journey a little in her Rebels s4 episode, where she helped Ezra let go of his master just like how she knew she had to let go of her own).
As you said, the series of unfortunate events that have unfolded upon Ahsoka since the Wrong Jedi arc have left her tired and probably hurting - as anyone would be. She’s lost so many people, and most of that has been because of the hubris of the Jedi, and her realisation that they’re not the heroes she thought they were as a youngling/younger padawan. Hence I would understand why she wouldn’t want to train Grogu in the ways of the Jedi.
I view Mandalorian Ahsoka as someone still engulfed in her grief. She is sad, alone and hasn’t received closure. The last time we saw her (not including the Rebels epilogue), she was limping down the steps into the shadows of a Sith temple after finding out for sure Anakin was one of the most “vile” Sith Lords in the galaxy. I wouldn’t expect her to come out of that feeling hopeful and restored (although, there has been a decade passed since then in the timeline, so I can’t be fully sure on that).
To me, I think her Return on Lothal, with the white staff and cloak, may symbolise her getting that closure - an overcoming of the hurt left from her battle with Vader and from the people she’s lost; a commitment to fulfil her promise to someone who she viewed as not dissimilar to her younger, pre-Empire self, reckless but full of optimism: Ezra. Perhaps with that comes a sense of selflessness, granting her the right to wield the staff which I’m sure possesses some kind of greater power.
She could even seek out Grogu at some point - this could be the long-awaited Luke and Ahsoka meeting.
I hope we see this journey in the live action show. It would be a meaningful, important use of a limited series dedicated to her. I could see it involving Mortis and the mythological elements of the force. Perhaps seeing Anakin’s force ghost, redeemed, may give her closure? I’d love if the last episode saw her arriving to meet Sabine from her point-of-view, sort of allowing the threads to meet and give a clear point to continue from in a Rebels sequel series.