It depends on the material that the fountain is made of. If it is real stone or cement (unpainted), glass, or unpainted plastic, then it is safe. However, if there is any sort of paint on it or you can't identify the material, then it is not safe. Paint used in decorative fountains often has lead or other heavy metals in it, which can cause serious poisoning if ingested.
Thank you. Most are resin, poly-resin/fiberglass, ceramic (yeah, painted), or copper. I found a plastic one actually made for animals, but doesn't look like it has much real bathing space. (No.7 Artisan Pet Flower Fountain, electric). Another fountain is made for a bird bath, but is solar powered, and I don't think it will work well indoors. Just researching options for a stubborn budgie