This 3D style is often times called “Gaslight Style” and falls into the Victorian design bracket. It’s thought to have evolved out of the optical illusions created by streetlights on storefront signage. The lights would cast shadows, causing the designs to look 3D.
Have a look inside the post for more history & examples…
“One pronounced aspect of Victorian design was a great interest in creating the illusion of depth, particularly so with lithographers. Type, vignettes, products and design elements are made to seem multi-layered through the use of shadows, superimposition, dimensional banners and ribbons, turned-up faux page corners and choice of colors. Some have labeled this the “Gaslight Style” approach to design…”Said to have derived from the play of lamps on three-dimensional street lettering [ i.e. storefront signage, etc. / ed ], the style appears to have originated in Germany, spreading, through the influence of German printing skills, throughout the world.” (Collecting Printed Ephemera, London 1988 p.116) Rickards describes it at greater length in his Encyclopedia of Ephemera(Routledge, NY 2000, pp.50-51): ‘Chief features of the style are heavily three-dimensional lettering with a vigorous rendering of tonal gradation and shadow effects.”
Via Sheaff-Ephemera. Check out their website for a more in-depth history of this style and a massive resource of examples.