SageMaker and VertexAI are the AI services of AWS and GCP respectively, and they both offer embedding generation and vector databases (the two key pieces necessary for embedding search).
There are a bunch of smaller companies offering vector search as a service too, example pinecone to name just one: https://www.pinecone.io/
I also just found pgvector which seems like it could help? It has a similarity search.
Alternatively vespa cloud [3] offer both but… not the easiest to work with, it's tailored for businesses where search is a primary component.
Feel free to shoot me an email (in profile) with your context if you have more questions, in case I can help
[1] This model is a solid baseline if you're working with English text: https://huggingface.co/sentence-transformers/all-mpnet-base-...
[2] OpenAI's embeddings is probably the easiest to get started, and the API is straightforward. It's not the best performing embeddings for retrieval but good enough in some cases: https://platform.openai.com/docs/guides/embeddings/use-cases