It all boils down to the question of what level of effort justifies calling a game a deluxe edition, a remaster, a remake, a port. How I see it, only one change in Ultimate could warrant calling it a new game (new campaign mode). But like I argued, it could also fit in the definition of a deluxe edition (example: brand new maps like the Ghost of Tsushima Director's Cut). All the rest (level texture and background quality, balance changes, new characters), all that is in line with the patterns of the DLCs or other remasters that were never called new games. So I, esp. having played Smash 4 a lot, don't feel like we can call it a new game, like I can't call Ocarina of time 3D a new game just because they remade ALL the textures in the game (yes, all, that's a lot of effort).
It seems your definition of what constitutes a new game is stricter than most people so I'm curious, what criteria in being a new game does Ultimate fail to meet in your view? My definition isn't strict since I generally consider remakes new games so the difference interests me.