I feel frustrated at my long distance friend
Hello everyone. Basically, I'm looking for advice on how to (politely) communicate to my friend that we're not as close as she thinks we are.
To provide some context, I'm a European uni student and here the Erasmus exchange programs are very popular. Last year, I was abroad during the spring semester with this program. There, I became really close with a group of girls and especially with one of them (let's call her Emily).
Fast forward to the last week of the program. I had a lot of fun, but I was also excited to go back home. One day, Emily got really emotional and started crying about how much she would miss me when she'd leave. I was honestly taken aback, because even though we were together almost everyday, we didn't exactly bond over anything, nor did we ever have very deep and meaningful conversations. She said I was her only friend and that her "friends" back home didn't care for her (which I found out was a lie, she has wonderful friends). To make her feel better, I promised her that we could face time each other, since our countries were kind of far.
A month after this, we started facetiming every week. It was ok, since I didn't have any summer classes at uni. But as September started, it became really time consuming. I told her that I didn't have time for it every week and we decided to facetime around once a month. Apart from the fact that the scheduling reminded me of corporate zoom meetings, our conversations were always a bit shallow.
She was very frustrated that we couldn't facetime more often, and because I replied to her messages after 2-3 days.
Then one day, out of the blue, she started basically traumadumping. She said I was "still her only true friend", but I felt very uncomfortable. After that, I started kind of ignoring her messages (not only because I felt weird but also because I had exams) and she got really angry with me. I imagined she'd stop talking to me after that, but nothing changed much.
A few weeks ago, she said she got me birthday presents (yes, plural) and she was really excited to give them to me when we'd finally meet. I have no idea when her birthday is, but she remembers mine.
I'll be honest, I'm at fault as well. I told her she was being pushy only two times in the past year, and it was kind of half-hearted. I'm aware I have issues with boundaries and I don't want to be seen as a cold person. I don't want to make her feel like I'm "abandoning" her, because I know the feeling, and it's awful. Since we spoke so often, I probably lead her to believe that we are close friends, and now I don't know how to explain that I see her more as an acquaintance.
It's evident that she has some issues but I know almost nothing about her, so I don't know how to handle this... Any advice? Is there a nice way of telling someone you're not really "friends"? I'm scared that if I'm too upfront about this, she'll stop talking to me altogether and I don't want it to lead to that. Thanks.