Yes we have it and it's called "carcerazione preventiva" but it applies before the sentence has been issued to prevent reiteration of the crime or further damages to society while waiting for the final pronunciation.

What I could imagine happening in Germany would be X years + unknown years “preventive detention”

Very unlikely. You don't get Sicherheitsverwahrung unless you're proven to be an extreme danger to the public in general. If you murder someone for specific reasons that's unlikely. Hence typically you'll need a long history of violent crime to get it, a single incident, regardless how brutal, rarely cuts it. We have some 600 people in Sicherheitsverfahrung in the entire country but some 700 homicides per year and tens thousands of non-fatal crimes that can be bad enough to warrant Sicherheitsverwahrung.

In Germany the guy would likely have gotten a life sentence (i.e. a possibility of probation after 15 years) but not why you think. Jealousy isn't necessarily a "niederer Beweggrund" / abject motive here either. If you kill for that you can get away with manslaughter. Here however the perpetrator used a state of helplessness and therefore meets the Mordmerkmal/ murder trait Heimtücke/treachery.

If you just shoot your spouse in the face after they told you they were leaving, you do stand a very good chance of getting away with manslaughter in Germany. I.e. 15-years max.

The German (and apparently also Italian) murder laws need to be reformed (e.g. in Germany babies are harder to murder because Heimtücke needs to be unsuspecting by choice but babies are inherently unsuspecting), but people getting comperatively low sentences for homicides committed in situations like breakups does make sense. It's scenario where people are highly emotional and less capable of thinking straight. Hence punishing them less harshly than people who do for example murder someone because they get paid to to so is how the law is supposed to work. The more sound your state of mind was, the more culpable you are. Punishments in our legal systems aren't about retribution, they're about influencing decisions so that crime is an objectively bad idea. Therefore it doesn't matter that much how bad the outcome was, it matters what decisions perpetrator made.