And if looks kinda like art nouveau
— with lots of lush flora, tiny insects (like dragonflies) or graceful birds, stained glass, iron, warm golden lighting, lots of wood and wood carving (but now it's more wood paneling), a stylistic fondness for Japan, line weight variation in the font, and tile (but this time it's carved or sculpted on, not tiny mosaic)
but you're worried it's art deco
— because the forms (especially foliage) are very symmetrical and slightly more angular or blocky and graphic looking, things are more rectangular than circular or curvy in architecture, the patterns repeat more often, and more of the lamps are pyramids or rectangular, and there are nods to Egyptian or Ottoman style, and they used the color red (probably in an accent chair or carpet rug)
BUT there's no steel, concrete, gold plating or gilding, marble, big muscles, spiky or radiating diamond shapes, angular people, or flappers,
AND the vibes are jacobean, gothic, or spanish mission revival; they love some brick and stone; the wallpaper is an explosion of colorful pattern that could give you arsenic poisoning or help depict a descent into postpartum psychosis in a famous short story; but there are NO people to be seen, not even sexy ladies,
— then THAT is the arts & crafts movement.