What are the 'notes' that appeal to her? Is it the setting, the art style, the story, or a mix?
Please don't think I'm being unserious, but how about Pokemon? Much more age appropriate than Demon Slayer and ties into the games. It hits the 'adventure' note, has battling and the current series, Horizons, has a female protagonist, if that's important to her.
Good luck finding something!
Yeah that makes sense. Unfortunately if it's the maturity that's appealing, then anything that's 'age appropriate' may seem uncool by comparison.
I guess with Pokemon, the trick could be just to put episodes on anyway and see if that can supplant whatever other shows she may have previously zeroed in on. There's a reason why Pokemon is as popular as it is.
If the show doesn't have to be recent but still would need to be that sword fighter type of anime, you could try to introduce shows like Rurouni Kenshin or Inuyasha when appropriate. There's still violence but not on the level of Demon Slayer. You can check the Parents' Guide (this one for Inuyasha) on IMDB for advice on content and themes. I guess it's up to you to determine what's right for your child, so please don't take these as out and out recommendations.
Edit: It turns out there's a 2023 remake of Rurouni Kenshin. Here's the Parents' Guide for that series.