Currently, ES and Solr, both based on Lucene, can't really manage vector representations, as they are mainly based on inverted indexes to n-grams.
ANNs potential applications extend to audio, bioinformatics, video, among any modality that can be represented as a vector. All you need is an encoder! How nice.
Faiss is definitely powerful. I have been running experiments using 80 million vectors that map to legal documents, and vectorizing protein-folds (using Alphafold). While it is an interesting technology, at this moment, perhaps for my usecases, I see it more as a lib or tool than a full-featured product like ES or Solr.
For instance, ATM, updating a Faiss index is a non trivial process, with many of the workflow tools you would expect in ES missing. There is also the problem of encoding the input into vectors, which takes a few milliseconds (do you batch, parallelize, are you ok with eventual consistency?).
I recently been found with pgvector (postgres + vector support) https://github.com/ankane/pgvector. Perhaps less performant, but easier to work with for teams. With support of migrations, ORM, sharing, and all the postgres goodies.
Another interesting/product-ready alternative is https://jina.ai.
And Google's ScaNN, https://www.youtube.com/watch?v=0SvrDtnUgV4