With what we know, there nothing to be worried about. The issue lies with the Bitwarden SDK, and not the Bitwarden apps or authenticator. The language is not entirely clear, but my interpretation is that they want to prevent people from using the SDK to create a Bitwarden app competitor. It sounds like they do want businesses to create their own, internally used client, and worded the TOS in a confusing way.

I gave AntennaPod a try and was blown away at the granular control you are allowed over everything. Its a fantastic app that set a new standard for what I look for in an other apps now.