"of course it won't show a curve because it's zoomed in."

If you zoom in to a ship and it appears it means that distance is flat at SEA LEVEL. If there's a curve it would disappear over the curve or horizon.

Regarding seeing faraway battleships. It depends how clear it is.

I will never forget many years ago the day after Thanksgiving me and a friend went fishing on the Oceanside pier in San Diego. It was such a beautiful day and clear. I was fishing off the north side. I cast my bait and was looking down the beach and watching birds and people then something very large appeared in my left peripheral of my vision and it startled me

There as big as could be was Catalina Island. In all my years I had never seen it from any beach in San Diego as I played a lot of beach volleyball and fished.

Why couldn't I see it before? Air moisture, fog and pollution. That day was a Santana which was dry and clear.

Here's a long camera shot.

https://m.imgur.com/IjtVyNw