What does Stamina Break do, and how can I tell if I did it to someone?
There's two ways to stamina break someone.
1) A new move called "Stamina Break" that you can perform by pressing either forward square or forward triangle; the square one is a gut punch (generally) the triangle one is one that knocks them down to the ground. This move completely gets rid of any stamina they had while stunning them for a few frames to give you a chance to continue to combo them. Think back to Infinite World or Burst Limit for something similar except in this game it directly impacts one of your resources. When their stamina is gone from this, it recovers a bit more quickly than the other method of breaking someone's stamina.
or
2) Breaking someone's guard and/or armor during a transformation/ultimate attack. If you charge a heavy attack (press and hold triangle) while someone is either guarding or they are transforming (generally Saiyans or Namekians only afaik, the others don't have armor during their transformations) or performing an ultimate attack (generally, not all ultimates have armor) and you let it go fully charged on their guard/armor, you'll notice a special animation plays when you've broken their guard/armor. That indicates to you that you have completely broken their stamina. It's similar to, say, how in Smash if someone has a small shield and you charge a smash attack you'll most likely break their shield.
Their stamina bar will go to zero and they will be vulnerable to attacks for a lot longer than the first method as the stamina recovers more slowly than the first one.
Breaking their stamina prevents them from:
Dashing
Snap Vanishing (aka escaping your combos/supers/ults)
Using Evasive moves (i.e Angry Shout, Explosive Wave, etc)
Block/Guard
You'll definitely notice in this game when you break someone's stamina as not only are there visual cues but you can also see everyone's stamina bar now.