I think the most advanced project regarding IDE integration nowadays is Merlin (
https://github.com/def-lkb/merlin ), which gives direct feedback on syntax and typing errors. It doesn't have any knowledge of unit tests or coverage checking, but it would probably be the right tool to start with to integrate such a feature.
Note that there has been a bit of back-and-forth on the instant feedback feature. Previous iterations were deemed a bit too visually invasive, and some people don't like to risk being interrupted by their IDE while they think about their code. I think it's always better to have the feature available, but there is clearly some tuning to have, and potential for overdoing it.
The other project that jumps to mind is the Why3 IDE (
http://why3.lri.fr/ ). It seems they're not hype enough to have video stuff available, but from what I remember the GUI does a pretty good job of giving feedback on how external provers run, and pieces of code that were previously verified and aren't anymore.