The fact that this sink doesn't have a channel for overflow from one sink to the other and has no other obvious overflow control is really bothering me...
They usually overflow into the other side of the sink. There is a raised rim along the outside, and the area between the two is very slightly lower. This means that the water will overflow into the other side.
Dunno about "usually". Our last house was fairly nice, but didn't have this sink feature. That said, you could walk around and see where the builder went for the cheapest option available.
That said, this kitchen sink feature should literally be the absolute minimum for consideration.
It's getting less common because it looks cleaner and functions better to have the divider flush with the sides. My sink is flat on top and it's better because I can set what I'm washing out of the sink. It does get scratched up over time though.
Cheap sinks have the rim they are describing. Expensive sinks usually have a low or no divider. It's the mid teir that is going flush on top for some reason. It's a completely useless feature IMO that makes the sink less useful.