Here is their video showing its manufacture and firing towards Ashkelon and Ashdod. They lovingly print "Made in Palestine" on each rocket.
Islamic Jihad is funded by Iran.
Notably, Houthi forces in Yemen also have domestically-made missiles dubbed "Badr" although they are different models. The latest ones are apparently precision missiles.
Badr was the site of Mohammed's first major victory against the much larger Mecca army.
Iran's Revolutionary Guards are prioritizing the design of missiles that can be built locally in areas that Iran wants to expand its influence. If Islamic Jihad can build the latest Houthi weapons, it would be a major advance and a worrying development.
Iranian media also heavily covered the Badr-3 launches.
The not-very-reliable Debka claims that the Badr 3 has a warhead that weighs 250 kg and a range of 150 km. It also claims that it explodes above the ground to maximize the area of shrapnel. Islamic Jihad is reporting but not confirming Debka's claims.