Replying in exactly that way, as if you’re a sentient observation bot, is probably not a good idea but the approach itself is solid. It’s mostly about context
I do agree. I am familiar with three levels of listening, but in a slightly different way where the three levels are more about where your focus is as a listener.
Roughly it comes down to:
1. Listening but focussed on yourself, interjecting with own experiences and sometimes in the process take over the conversation with your own experiences.
2. Focussed listening but on a factual level. Asking clarifications about events, etc.
3. Focussed not only on what is being told, but the emotions behind it. Asking about how certain things impacted the person sharing something with you.
I am hugely oversimplifying here, of course. But for point 1 it doesn't mean that you can't briefly let someone know you have a shared experience. It does mean that you shouldn't make your experience take over and then dominate the conversation.