What If : Henry V, Holy Roman Emperor, succeeded by Frederick I, Count of Zollern?

In 1125, Henry V, the last Emperor of the Salian Dynasty, died without Issue and was succeeded by Lothair III of the Supplinburg Dynasty. However, there was one person who Henry might've favored more to succeed him if he was still alive by the time of his death : Frederick I von Hohenzollern, Count of Zollern (who succeeded his father or Grandfather Burkhard I, dying sometime before 1125 at an unknown age (let's say he died in his mid 50-early 60s for the sake of the scenario). Frederick was the second of the Hohenzollern Dynasty, having succeeded Burkhard I in 1061 after he died in a duel. Frederick has been cited as a powerful Swabian Count that helped Henry V become Emperor and he was also the first reeve of the Alpirsbach Abbey in Swabia. He served Henry V loyally, having been sent on a diplomatic reason to France, and then accompanied Henry on his Italian expeditions while also serving as an advisor to the Emperor.

So it's clear that Frederick I seemed to be a favorite of Henry V but him dying before Henry did likely put a halt to any plans of Frederick potentially succeeding him or the Hohenzollerns reaching high levels of power quickly. So what if Frederick was between 57-64 when Henry V dies in this alternate timeline, still kicking, and he is able to somehow succeed in becoming the Emperor (he convinces the Electors to place support behind him instead of everyone else), becoming Frederick III. What's next for the Hohenzollerns and the HRE? Since he has only a couple years of rule, I think he'd be focused on securing succession for his son as Emperor.

Also, any idea what might come of Swabia from this scenario? I can see the Hohenzollerns using their prestige to strongarm the lesser counts into making them the ruling Ducal family of the region.