In my mind, the greatest strength of a flavor ability is to accentuate the least prevalent flavor aspect of our design. In Jumbao's case, it has a lot of requirements to fulfill, and it does so reasonably well on most accounts. Grass-type is the most obvious aspect it presents, while Drought and sun support fall in line well with the baobab design. Its stats follow the design pretty well, in my opinion, and its movepool helps give credence to sand support.
I personally feel that Jumbao represents Fairy-type the least of all of its attributes. Yes, you can talk to me all about its shimenawa until you're blue in the face. And I would agree with you that it is great flavor, but I'd also argue that it isn't entirely accessible as a design choice. You have to know what a shimenawa is, which I certainly didn't until pipotchi made the design. Maybe I'm in the minority here, but none of my real life friends could tell you what the rope necessarily is. As a result, every single one of my friends has guessed that Jumbao is Grass/Fighting. Maybe it's the Makuhita in their brain influencing the choice, but try asking your friends what typing you think our newest creation is.
I don't think it would hurt us to accentuate Fairy-typing by any means necessary. Cute Charm is the obvious stand out here -- seven of the fourteen Pokemon with this ability are Fairy-type. Only one of them is Fighting-type, and that'd be Stufful, which I don't think really needed the ability anyways to be considered cute. You may think that Cute Charm is only given to cutemons like Wigglytuff and Cinccino, but it also has a user that I think is a great flavor equivalent to Jumbao: the Water-type Milotic. It's a cool design full of mystic and power, and it too gets Cute Charm (along with some other cool abilities).
If you can think of another ability that would better bring out the Fairy-tying of Jumbao, please let me know. All of the Fighting-type implied ones are completely off the table for me (Justified, Inner Focus, even Vital Spirit). Things like Honey Gather and Leaf Guard are fine, but Grass-typing is already super obvious on Jumbao. Own Tempo is alright, but it suffers the connotation of a slow Pokemon, which is something Jumbao struggles with as a design (social media has been keen to point this out). Adding an ability that implies slowness only harms us; look at all the crap Purugly gets for its speed. Overcoat is alright, especially since it helps bring out sand in the design, but then you might as well argue for Sand Veil if that's your ultimate goal. I personally think the ability to avoid chip damage is too competitive for a flavor ability, but I guess that is your call to make.