Am I understanding this correctly, that she is the first Japanese vessel introduced to survive to the present?
Yep. The IJN suffered heavy attrition, with most of their large ships sank during the war or scrapped immediately after. Then they had to turn over all their remaining combat-capable ships to the allies; ships transferred to the USSR or RoC sometimes had lengthy careers, but ships transferred to the US or UK were generally only considered useful for target practice. Souya escaped either fate because she was an ice-breaker-turned-freighter, so nobody cared if Japan kept her. And then they made her into a museum ship. And considering how many close scrapes she survived during the war, I can see why she'd be considered lucky even beyond Yukikaze.