Celebrating her birthday was unfamiliar
No, the idea had to be introduced
(reintroduced, rather)At one point, she did celebrate it
But that was a long time ago
(when she was five)Since that time, it was just a mundane day
Mundane, just like her name
(about as "mundane" as she could define)But she did remember a wish she made
Many years agoShe wished for someone
To celebrate her birthday with her
(knowing of her existence made her birthday feel hollow)Such wish seemed impossible
Until recentlyHer birthday came
And she was given, of all things,
A seashellHer sister wasn't sure what to get her
Unbeknownst to Sister, she already had a gift
Her birthday wish was granted.
—Amoridere, 12/31/2022Authoress Headcanon: My headcanon for Satsuki's birthday is that she was either born in January (like her voice actress', Ryoka Yuzuki) or that she was born in May (as her name would suggest, presuming Souichiro gave her the name—He names things accordingly). All I know is that she was likely born earlier in the year and Ryuuko would be born later, considering their age difference.
Anyway, as far as why Ryuuko would give her a seashell, IDK, but I picture Ryuuko having a collection of seashells.