Developer Lao Ye claims the latest Codex update actively detects which model provider you're using. Switch to a third-party API, and the client may stop loading tools like image generation and web search. The model itself isn't any different — it's the client that loses capabilities.
https://twitter.com/1999_eth/status/2077447760673173538
According to their testing, changing the provider name to "OpenAI" restores some features, but enables remote conversation compression. Long chats trigger extra calls to /responses/compact, which could cause your proxy to time out.
Another workaround: keep the custom provider but add the x-openai-actor-authorization header. Codex's open-source test code shows this config re-enables web search and image generation.
Codex CLI and app-server are open-source, but the desktop client itself isn't. This "stealth downgrade" is still just one developer's reverse-engineering conclusion — OpenAI hasn't publicly responded.