You want to know, request by request, which servers see your prompts and captures.
On the free and Sync plans, requests travel from your browser directly to the provider, such as OpenRouter. Omni's infrastructure is not in the path, which is what makes the claim that your data is never seen a fact rather than a promise. Sync buys template storage, not inference. Only the hosted tiers, Pro and Max, route through Omni's proxy, and only so monthly spend can be metered with caps.
If you want the direct path, stay on free or Sync with your own key. If you prefer hosted convenience, Pro and Max is the right solution for you.