I got a chance to speak with him prior to the season (perks of covering a AAA team). Nothing too groundbreaking, but the fantasy relevant info is that A. The movement increases his changeup had seen slowly build up were due to minor tweaks, but not a wholesale grip change or anything line that, and B. He's working on incorporating his curveball more. I haven't checked the numbers since his promotion to see if these trends have continued.
Profile-wise, I like to think of him as a poor man's Kyle Hendricks. His changeup is very good, but not elite like Hendricks'. Ditto for his command. Both took statistical steps forward upon incorporating the curve more often (though obviously small sample for Bergman).
His pitching coach in AAA, Lance Painter, is in my opinion among the best in the business and seems likely to land an MLB job in the near future. He particularly excels with the finesse types (although his most prominent success was James Paxton - the opposite of "finesse"), so it's possible he unlocked something with Bergman, who's been a revelation in AAA (2.17 ERA and five wins in fine starts).
I think Bergman definitely has AL-only value and is a solid streamer in mixed. He's got a good defense and park behind him and a pretty decent offense. The bullpen will really hurt him though.