The only specific model name that will be deprecated is chatgpt-4o-latest - which is a copy of the gpt-4o version that ChatGPT ran, and the deprecation notice only refers to that one model on the API.
You should not have products built on the constantly-varying “latest” or “chat” version of a model. It is going to be unreliable, as OpenAI will tweak ChatGPT without regards to API developer applications.
gpt-4o itself continues, and if it were to be deprecated, the notice would likely be on a longer six or twelve month timeline.