I think eating a grocery store cake for your own birthday is sad in general. Bake a cake at home. The only time I ever get grocery store cakes is for some like a large kids party at a trampoline place

Your colleague sounds young. How old is she? Certain things I wouldn't have done when I was younger like going out to eat alone or buying my own cake don't phase me now that I m 48. Rules change and you care less about norms as you get older.