Actually, the typing activity is working in Bot Framework Composer, you can also see it in action here: https://youtu.be/wG8emu4v6hk?t=955 (brief moment at 15:55). The sample source can be found here: https://github.com/vishwacsena/composer-build-2020/tree/master/Birthday-bot2

The activity is sent the exact way you describe, but it is only shown until the next response has been sent. In the example screenshot, the delay is caused by the HTTP request, and during this time the typing activity is shown. If your responses are following each other quickly, you might not see the typing indicator at all as the process goes too quickly.
[Activity
type = Typing
]
I was able to simulate the above as well in my own Bot Framework Composer project, where I used a custom action to simulate a short delay. During the delay the Typing activity is shown.