I would only recommend pgvector if you're already primarily relying on postgres and the scale is limited (<1M documents). It won't handle the part that generates the embeddings though. You could use cloud vendors if you're in one of their ecosystem, do it yourself [1] (but model serving can be tricky without prior experience in ML), or use some other service to generate embeddings [2].
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