It's night from sunset until dawn. And if someone said "in the morning" I would never interpret that as meaning before dawn.

It is controversial, because one definition of "morning" is dawn to noon and another is midnight to noon. And saying "night" is "sunset to midnight" is also new because you just came up with that.

Morning and predawn are typically the times immediately surrounding dawn, not the time immediately after midnight.

If you told me "were going out to take photos at predawn" I'd assume you meant blue hour photos, not moonlit photos.

Right.

But 00:01 is clearly still night. Night is typically considered from dusk til dawn.

So if we say "the night of the 2nd" then that's from dusk til 23:59:59 of the 2nd.
Which is then followed by night that isn't the night of the 2nd nor night of the 3rd.
And I'd say "before dawn" or "early morning" of the 3rd would be problematically ambiguous.

I mean, I'm having fun arguing pedantics, but this is a pretty silly post. There is no room here for real practical solutions!

Right, but then how do you refer to before 5am on the 5th?
That's not morning, and it's not the night of the 4th. It's awkward.

But more importantly, it's ugly. It's not how we intuit about days. It's unsatisfying.