Yes, most Kami are probably not at the level to be invited to the celestial realm like most Kami did not reside in Takamagahara in Japanese mythology. The Amatsukami were mostly the direct children of Izanagi and Izanami with Amaterasu, Tsukuyomi, and Susano-o being the most notable three. While most Kami existed within natural features, shrines, or other areas that were attuned to their natures the Amatsukami specifically existed in a divine realm separate from reality which has overlap with the nature of celestials and their realm. I wouldn’t imagine that more than a handful would get the invitation because Kami are usually bound to nature and thus the transition would be at odds with their “essence” and we’ve already seen celestial foot soldiers and they feel a lot more like Modrons from D&D with their rigid adherence to their rules/procedures than how most Kami are reflected.

TL;DR: I agree that most Kami are not celestials, but the most important ones probably are and if the sunburst in his eye is indicative of Amaterasu then I would be more surprised if she isn’t a celestial if a Kitsune like Yuuki is.