Am I wrong for approaching her friend first and possibly making things awkward?

There’s a girl at my university library that I’d seen around for a while. We’d occasionally sit near each other and I said hi one day and had a neutral convo about her program and stuff. I eventually wanted to ask her out for coffee, but didn’t know how to do it directly.

One day when she stepped away from the table, I ended up talking to one of her friends. I was honest and said I thought her friend was cute and didn’t really know how to approach her. The conversation felt casual and friendly. Her friend told me she wasn’t seeing anyone.

A few days later, I gave that same friend a short note to pass along. It basically said: “Hey! I’d love to take you out for coffee this week. Text me if you’re into it :)” I included my number. I never got a response.

After that, things felt different. The girl started avoiding eye contact, staying close to her friends when I was around, and at times positioning herself behind them. Her body language seemed nervous or closed off. Over time, I stopped seeing her at the library entirely (it’s been over a month now).

I also tried to completely step back. I haven’t approached her again or tried to contact her in any way.

Today something else happened that made me question things. I sat down at a table next to another one of her friends (someone I’ve never spoken to before). When I sat down, she packed up her things and left almost immediately. That made me wonder if I’ve somehow been talked about negatively or if I made the situation more uncomfortable than I realized.

I genuinely didn’t intend to make anyone uncomfortable. I thought going through a friend would be less direct and less intimidating, but now I’m wondering if that actually made it worse.

Am I wrong for how I handled this? Should I have just approached her directly? Or am I overthinking normal social behavior?