Per § 86 StGB (our penal law) up to three years in prison or a monetary fine.
People would be outraged, of course only those that aren’t too far gone to the right. The reaction of the AfD would be most interesting, as they will probably like it but can’t make it too obvious, they’re already under watch by the interior secret services of the Verfassungsschutz.
Would anything happen to Musk? The richest man in the world, backed by a country with a law to invade The Hague when service members are kept there? Yeah, I doubt that.
There’s been a singer that did it during a concert. Multiple times, too. She got a fine of 80.000€.
Another one is this case. He got a fine of 600€ for showing the salute with the left arm. Reasoning of the person that did it:“I thought it wouldn’t be forbidden with the left, I wanted to be provocative towards leftist protestors”.
I found another one where an artist who did it in public was fined 30 “Tagessätze” (your daily income) worth 50€ each, so 1500€.
So most punishment comes in the form of fines, imprisonment is rare. One must consider that usage of the Hitler Salute is covered under § 86a of our Penal Code (“Usage of Signs of anticonstitutional and terrorist organisations”), which is more tame than the § 130 of the same code, “Volksverhetzung”. That one would always be met with imprisonment (three months to five years), assuming you’re the instigator. But the bar is also a lot higher, since it requires you to actively sow hatred, instigate violence against certain people, be it based on sex, heritage, politics, birthplace, religion or whatever.
§ 86a StGB in English
§ 130 StGB in English