The commentary refers to "The Great War of Archimedes" (アルキメデスの大戦), a live-action historical drama (from a manga of the same name) about the construction of the Yamato, which came out in Japan last week. It seems Nagato and Akagi make cameo appearances.

I think Nagato is being measured for the dress she'll be wearing to her red carpet debut?

The drama is actually about measurement and estimation of Yamato. The IJN headquarters plan to build a huge battleship, which is later named Yamato, but Yamamoto Isoroku doubts its unreasonably cheap estimation. He invited a mathematical genius Kai Tadashi to the Navy, and asks him to reveal the discrepancies between its specifications and estimated cost by measurement and calculation.