There's nothing wrong with what you have and I'm sure it could make an interesting backdrop for your story, but as plenty of others have noted, this is only a setting concept. It still needs a cast, plot, and themes.
You are- of course- free to approach the process of coming up with your story however you like, but my general advice to any writer would be that the story should come before anything else. A setting is just a backdrop that supports the story you want to tell and helps convey whatever themes you're going for.
Plenty of writers start with a fun idea for a character, a setting, or a "what-if" scenario and are able to build a solid story inspired by that initial concept, but I don't see any point to fleshing out your world to this extent before knowing what kind of story you want to tell, because once again, your setting is nothing more than a tool that exists to help you develop your story and themes.
This setting already hints at potential plotlines and themes. I just think you make it a bit more difficult for yourself putting so much effort into developing a world for a story that doesn't yet exist. It's like... making a beautiful, elaborate wedding dress without knowing anything about the bride's tastes or measurements. You might have to start over from scratch when you get that necessary information, so why waste your time putting the cart before the horse? If that makes sense. I dunno.
Anyways, it's hard to answer your question of "is this enough to start a story?", because whether this setting concept is 'good' or 'bad' directly depends upon the story you want to tell. On its own, it doesn't really mean anything yet.
I'll answer "yes" though. I think you should start brainstorming a plot, and fit the setting to whatever you come up with as needed.
My only feedback on what you've shared is that it's just fine. The kinds of themes (strict gender roles = bad) it could be used to explore have been done to death (every theme has been done to death), but depending on the story, characters, and execution- it could be really interesting and provide new insight, or end up trite and dull. No way to know yet, though.