Yep… Tsukasa is just a normal girl, other than the fact she’s been 16 for at least a thousand years, I think? She’s not been eternally 16, just ever since she drank the elixir.
She just wants to experience normal girl things. She‘s not actually anyone really special. She’s just got this whole immortal ever since her 16th year of life thing when she drank the elixir that was meant to be destroyed on the Emperor’s orders after Kaguya-hime left the first time. I don’t know the why of her getting the elixir instead of it being destroyed, but maybe it was a life-threatening injury or illness, and her father, just some soldier, defied the imperial order to administer the elixir to his precious daughter.