Jessie (Switch) appears as one of the Miis that are fought in the Sephiroth DLC Spirit Board in Super Smash Bros. Ultimate since update 10.1.0, and she hasn't appeared in any game since. Her Mii data file filename is edge_spirits_mii07.bin, with "edge" standing for Sephiroth.
She is based off a character in Final Fantasy VII with the same name. That character is allied with a group called the Avalanche, and Jessie is crucial to the bombings of some enemy bases. She shares this with Wedge, Tifa, Biggs, and Barret.
Her Mii name in her Mii data file is ジェシー.
Her Mii ID is as follows: 37 6E D4 F2 50 F1 41 F8 9C D7 DE 2F 48 AF ED B0
Her Mii data file contains unused Mii data. In-game, her Smash color is set to black (as Smash Ultimate can save a favorite color separate from a Mii's actual favorite color), but her Mii data file has her favorite color set to red.
Jessie (Switch) makes an appearance in one spirit battle, unlocked on the DLC Spirit Board if Fighters Pass 2 or Sephiroth's DLC is purchased. She will appear in the spirit battle for the spirit "Barret" holding a Bob-omb (to reference her explosive specialties in Final Fantasy VII/Remake), alongside Wedge and Biggs, and after all three are defeated, Barret. The Barret Mii Fighter must be defeated for the player to win.
Her Smash color is black, and in battle, she always appears as a Brawler and wears the Protective Gear with no headgear. Her neutral special is set to 3 - Exploding Side Kick. Her side special is set to 2 - Suplex. Her up special is set to 1 - Soaring Axe Kick. Her down special is set to 2 - Feint Jump. (Moveset: 3212.) You can see a screenshot of how she appears in-game on the left.
Jessie (Switch) unfortunately does not appear as a Mii in any promo art released. However, she does appear as her human character in promo art for Final Fantasy VII Remake, which can be seen on the left.