I need some information about how the stream title functions.

What we need here is when a Dj or another live source (sam broadcast) is connected, the “stream title” should take the song title from SAM.

In a different case, if the Auto Dj is connected, the “stream title” should have a predefined title.
I observe that, even with the auto dj in “disabled” mode and not simply “stopped”, in the stream title appears the predefined text. In settings->stream overrides I have set the %s.

I would be grateful if you could explain how the system works in this part/detail.

This is not a bug.

If under "Server overrides" you have the "Stream title format" set to "%s", then DNAS will display whatever text is provided by your streaming source (SAM Broadcaster, the autoDJ, etc.)  If you're using a live source and it's not displaying what you expect, that will need to be resolved in the metadata settings in your live source (eg: SAM Broadcaster).