> If their website/service disappeared off the face of the earth tomorrow, would I still have access to my passwords locally?

They provide a selfhosted alternative to their cloud service.

Not only that, there is a rust based birwarden server reimplementation that doesn't phone home (IIRC I believe the official self-hosted server needs an API key?), is compatible with all platform clients (at least for my needs). https://github.com/dani-garcia/bitwarden_rs