Spoiler alert: the answer is maybe! Although, my inclusion of the word “actually” betrays my bias.
Vector databases are having their day right now. Three different vector DB companies have raised money on valuations up to $700 million (paywall link). Surprisingly, their rise in popularity is not for their “original” purpose in recommendation systems, but rather as an auxillary tool for Large Language Models (LLMs). Many online examples of combining embeddings with LLMs will show you how they store the embeddings in a vector database.