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Arts & Crafts also developed into the ornate art styles of Art Nouveau and Art Deco.

Those are still modernism! They may be more ornate than than a Mondrian painting or something, but they sure aren't "ball and claw foot" ornate.

From https://en.wikipedia.org/wiki/Arts_and_Crafts_movement :

Some consider that it is the root of the Modern Style, a British expression of what later came to be called the Art Nouveau movement.[4] Others consider that it is the incarnation of Art Nouveau in England.[5]

Also, for that matter, from https://en.wikipedia.org/wiki/Art_Nouveau :

The term Art Nouveau was first used in the 1880s in the Belgian journal L'Art Moderne to describe the work of Les Vingt, twenty painters and sculptors seeking reform through art. The name was popularized by the Maison de l'Art Nouveau ('House of the New Art'), an art gallery opened in Paris in 1895 by the Franco-German art dealer Siegfried Bing. In Britain, the French term Art Nouveau was commonly used, while in France, it was often called by the term Style moderne (akin to the British term Modern Style), or Style 1900.[9] In France, it was also sometimes called Style Jules Verne (after the novelist Jules Verne), Style Métro (after Hector Guimard's iron and glass subway entrances), Art Belle Époque, or Art fin de siècle.[10]

Art Nouveau is known by different names in different languages: Jugendstil in German, Stile Liberty in Italian, Modernisme in Catalan, and also known as the Modern Style in English.