Vector searching had strange quirks where searching for "cat" would return mostly a lot of paragraphs unrelated to the word. I was using 3072 length for OAI text-embedding-3-large. Each entry was roughly 1-2 paragraphs. For my recent project, I found that PGroonga was more reliable for full text document lookup (with some fuzzy matching support).
"cat" is not a sentence - the embedding should be close to other contextless single words, and maybe just slightly closer to paragraphs about cats than paragraphs about non-cats.
A simple way to use embeddings for search is to generate text of the same kind you expect your users to input - e.g. if you expect users to ask questions in natural language, have a cheap LLM turn paragraphs like "Cats are natural carnivores." into questions like "What do cats eat?" "What is natural behaviour for cats?" and then index the embeddings for those.