Terragon is an alternative (hosts Claude and Codex using your OpenAI and Anthropic subscriptions, and also supports Google and Amp) that provides this functionality.

I use it because it works out cheaper than Codex Cloud and gives you greater flexibility. Although it doesn't have 5.2-codex yet.

Yes but if it's not getting removed at the origin... it's not fixing the actual issue of the context/conversation surviving past an explicit "delete" request. Also let's not forget that anyone proxying LLMs is also man in the middle to any code that goes up/down.