She struggles with confidence in the beginning (Cerulean Blues) as she’s thrown into a tough situation with an unruly Gyarados and the gym potentially being shut down, but ultimately she pulls through and is proud of herself. In fact, she asks Nurse Joy to tell Ash that she made it as a gym leader. 

In all of her other chronicles episodes, she is shown to be doing very well adjusting to her new role. The only instance that might show her pining over Ash, although the English dub almost completely eliminates it, is when a secret admirer asks her out on a date. She declines his effort and in the original version, it is hinted that there is “someone else,” but this was never elaborated on further. It is also worth noting that Tracey visits her in all but one of her episodes and her sisters have returned home soon after she gets there. 

When Misty meets Ash and Co. in Hoenn, she went for a [fake] Togepi festival where she seems very happy, yet very busy at the gym. Yes, she is shown proudly watching the Hoenn League on TV, but same with everyone else from home (his mother, Professor Oak, Tracey). Just like how Max, Drew, and Harley were shown watching the Wallace Cup on TV in May’s Sinnoh arc. When she meets him at his house after Hoenn, I supposed that could be seen as a pining moment, but knowing that she is still in touch with Tracey, in my opinion, makes it seem less about missing Ash. She is still clearly embracing her responsibilities of her role, since she is shown to be quite uneasy about leaving the gym in her sisters’ hands for more than a short while. 

While, yes, many fanfics do portray her as sad and lonely in the gym waiting for Ash to come home or wishing she could travel with him again, This is strictly a headcanon, since the show’s canon shows her happy at the gym and unwilling to leave again. I also feel like for every “Sad Misty” fanfic out there, there are just as many [in my opinion] better ones where she has a new goal of becoming a member of the Kanto Elite Four, giving her more to strive for. But that’s the beauty of imagination, nothing is right or wrong.