IMO, the reason is that sad tab view can't get focused.

Your analysis is correct.

I think this behavior is OK.  The only real way to fix it would be to make the sad tab area able to take focus, and I don't know that that buys anything.

I thought this was strange because omnibox popup behave differently on both - normal and sad tab.
Do you mean that different popup behavior on both looks ok?

It behaves differently on a normal tab because you're actually giving the page focus and the omnibox is losing focus.  The cursor disappears.  Your selection disappears.  And, if the dropdown is open, it closes.

When you're on a sad tab, there's no web content -- that's a native control.  Admittedly, this is an implementation detail, which is why I said we could try and fake this by making it focusable.  But there's no real user benefit to being focusable.  It just looks a bit inconsistent.  So it doesn't seem like it makes sense to spend the effort to do this.

So I'm OK with the different behavior.

Ok, Thanks for your answer!