Do @-mentions work with the API?

If not, is there a plan to integrate @-mentions for linking external GPTs into Assistant’s API threads in the future?

No, no. As for plans, I can guess no.

The API is for developing applications with your own code.

Not for developing applications with GPT user’s code and API actions that run against other developer’s sites, that others have written and may expect to monetize.

You could program everything you see in ChatGPT yourself. The key being the yourself part.