There's actually a historical reason for this - all of these are examples from the Modern Era and this is a specifically a feature of Modernism and the Modern Era more broadly. Firstly most of the names for pre-modern art movements are retroactively given. It's usually hard to recognize a wider movement while living through it. For example term like Gothic or Romanesque art or architecture were not used during the Medieval Era, rather they were seen as multiple styles, like "Tuscan", "Saxon" and "Norman". In the Modern Era, when the scientific method influenced how history was written as well, and historical art and architecture started to be cathegorized into taxonomical styles, it also influenced how art was made after that. The interest in archaeology and the antique world inspired stylistic emolation of antiquity, but also the taxonomical lens people now used to examine art led to intentional naming of new movements. They would say "I'm not doing that old vulgar art (baroque) I'm doing Classical art". When you want to name your new art movement you're specifically contrasting it with the other older art, otherwise there's not really much need to come up with a name. So it's not surprising many would call their art some sort of "new art", but it's not just that.
Enlightenment philosophy set the tone for the whole Modern Era, and one of it's core ideas is the linear understanding of time and progress. This was taken to it's logical extreme in Modernism, in which new is always better. It was not called modern only to contrast with revival styles which borrowed from history (I wouldn't put these Neo-Gothic etc styles in the same bin at all since they were usually called at the time Gothic Revival etc), but also because newness was core part of it's identity. Art Nueve, Jugent etc. were the same art movement in different countries, which was literally New Art in different languages, and it was the first Modernist style. It could be described as pre or early Modern since there were still some differences to what would become Modern Art, but it was early form of the same movement and it had the same underlying ideas that Modernism would adopt. So when a distinct style inside the Modernist framework was developed, it's no wonder it was often called some version of new, since newness itself was the aim and purpose. Now we're in the Post-Modern Era, where we're trying to move past Modernism, but we're definitely still somewhere in that Modernist framework, so everything is New but Not Like That.
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