Big companies who are extremely protective of their secrets use the cloud. Even the US government isn't afraid to store classified information in AWS, and they're not joking around with secrecy.
Unless you're acting specifically against American interests, I can't imagine a situation in which a cloud company would actually steal your secrets.
If anything, I'd be afraid of a vector DB vendor getting hacked, but I don't think that most non-tech companies who want to use vector embeddings for their documents can provide better security themselves.