I haven’t played Overwatch or Minecraft but every game I’ve played with one of those options used pressing in the touchpad to do that. I’ve never played a game where the share button didn’t share somehow.
I just looked it up and for Minecraft it’s used to take a screenshot or bring up a screenshot menu. I couldn’t find anything for Overwatch though. Are you sure you didn’t remap the button? Or are you using it for PC? It might work different in that case.
I do agree that menu would’ve been a better name, but that doesn’t mean that Options doesn’t make more sense than Start which is what the original comment said.
I think it’s specifically a PS4/PS5 thing. I couldn’t find other controllers with an Options/Share combination. And I imagine if you use a PS4/PS5 controller for PC, it handles it differently. But it makes sense since the controller wasn’t designed for that.