Google Vertex appears to support no logging in general (assuming the abuse logging is opt-ed, although, their logging policy has been hard to locate). I've also noticed that Google Vertex added Claude to their partner models list.
https://docs.cloud.google.com/vertex-ai/generative-ai/docs/partner-models/claude/opus-4-6
It seems booth Amazon Bedrock and Google Vertex have a no logging policy (or at least Amazon claims no human review). Anthropic seems to have the longest retention policy (30 days, up-to 2 years). I wonder if it would be optimal (most private) to route the majority of queries over Amazon Bedrock and Google Vertex, using Anthropic for completely new models and as a backup.
It's not clear if Kagi has opt-ed out of logging on Google Vertex. And it's not clear what retention policy that Google Gemini API has (is 30 days from internal communication with Google?).