Should I store embeddings in the same document as the data?

I was using OpenAi text-embedding-3-small, which was working fine, taking maybe 2 seconds to return the result. I am using the embeddings within the result for post-processing and displaying debug information. I switched to text-embedding-3-large and my site now takes ~25 seconds to return the result. If I remove the embeddings from the projection, it takes ~3.3 seconds. If I download the associated embeddings myself after the query, then I get get the total time to ~5 seconds.

I’m not sure why including the embeddings in the projection causes such a massive slowdown (possibly server memory and paging?), but that’s what lead to my train of thought, if I’m having to retrieve data after the query anyway, then why not just use the embeddings and _id in a collection and retrieve what I need afterwards.

I could try reducing the embedding size to 1024 from 3072, but then I obviously lose context.