What it does
The same mechanism one layer down, without the orchestration modules around it: the documentation states that the AzureOpenAiChatClient supports streaming response for chat completion requests based on the server-sent events standard, with the client constructed on a deployment.
Remaining work
Carry the chunks onward, as above, and accept that the templating, masking and filtering the orchestration client applies around a call are not here, so anything of that kind is the application's own code.