I do not understand those references.
I think in Season 1, they made a strong case that Tilly was the smartest person on the ship, but was held back by anxiety issues. I think they're still building her up, but she's definitely more confident now she's got an actual rank and is on the command track.
Looking at Wikipedia, I think you're trying to imply she's shrill and annoying. I don't really think she is. As I said, she's very intelligent, and extremely awkward - not an unknown combination. She seems to be using an outwardly positive attitude to cover up not only self-doubt, but also a less than happy home life. (See the pre-season "Short Trek" featuring her.) Again, not an unknown coping mechanism.
Maybe I like her because I identify with all her emotional and psychological issues. Or maybe I'm projecting to some extent. I still like her as a character. I like most of them to some extent, and at least Tilly hasn't started any wars, or tried to kill any of her crewmates, or slept with a Klingon spy, or lost complete contact with reality...