Yes. You can build third party applications on top of codex app server. All open source. https://developers.openai.com/codex/app-server/

By default, assume no. The lack of any official integration guide should be a clear sign. Even saying that you reverse-engineer Codex for apps to pretend to be Codex makes it clear that this is not an officially endorsed thing to do

Interested to know this too

Why does it matter to the free buffet manager where do you consume the food? We may never know.

They'll own entire pipeline interface, conduit, backend. Interface is what people get habitual to. If I am a regular user of Claude Code, I may not shift to competitor for 10-20% gains in cost.

They must be getting something out of it, because we sure aren't.

They want that sweet vendor lock-in.

Presumably because their flat rate pricing is based off their ability to manage token use via their first-party tools.

A third-party tool may be less efficient in saving costs (I have heard many of them don't hit Anthropic LLMs' caches as well).

Would you be willing to pay more for your plan, to subsidize the use of third-party tools by others?

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Note, afaik, Anthropic hasn't come out and said this is the reason, but it fits.

Or, it could also just be that the LLM companies view their agent tools as the real moat, since the models themselves aren't.