Others have mentioned that Braun was absolutely buried last year and didn't do too badly.
I think another issue is that the Vlasic-Braun pairing was getting a little stale. They were doing this thing where Braun was taking all the physical punishment...anytime the puck was dumped down Vlasic's side, they would switch so that Braun could take the hit while moving the puck to Vlasic. That wears on a guy over the course of the season, and resultantly, he had a disappointing playoff run.
He's obviously not going to be doing that with Dillon, and it would be nuts if he faced top competition. That would be a great third pairing as you have two big bodies who can skate and pass the puck reasonably (in Braun's case, very) well.
However, it is a poor fit for the player and the team. The Sharks could free up his nearly 4 million in salary for 2020, and Braun is underutilized off the 2nd-pairing and 1st PK. Braun also is offensively capable and really should be getting secondary PP time, but he's not going to get that in San Jose.