Put a post and, if needed, a railing there.

Yes, that needs a newel post and redo the rail to connect.

I like the new detail better.

I think it is fine as long as the railing is the right height. No one is going to be walking so close the wall that the little jog becomes a tripping hazard.

It looks great! I dont think it will be a problems unless you have very young children, guess then you would need a gate anyway.

Note where handrail should begin & end. Have the handrail built to code.

That looks dangerous but the post & railing there before looked odd.

I would probably furr out wall with a low narrow built-in bookcase that matches the trim to block off that gap by functioning as a railing.

Or put a narrow piece of furniture there and bolt it to the wall for a guard.

Thanks, If I'm reading @MDLN post correctly, the handrail is not to code. That's what I was afraid of. I will ask the builder on Monday. It's strange because they talked about code (continuous railing and height....) as my old stairs (built 1973) were not to current day code.

I will speak with the builder on Monday.

If inspection passes this, I wouldn't worry about it.

I would want the post and railing there. The bookcase is a good idea, but, it appears, you have a doorway there, and a bookcase would not work. It is a safety hazard the way it is now.

For safety, you should be able to easily grasp the railing BEFORE stepping down the stairs. With this positioning, would have to bend forward, or step down to grasp the railing = not safe.

You paid for a new staircase, it should be safe!