This part is true. If she wants to be with you, she has to make an effort to change. Even if she's apathetic toward her phone, there's still email, at least. If one thing doesn't work, she has to be open to trying other things. It can't be just "I have a problem with responding, period" because that indicates there's no solution unless you're magically "special enough" for her and maybe she doesn't even know what that looks like.
Both my husband and I are normally apathetic toward our phones, but now that I work outside the house, we've both discovered the magic of texting emojis.
It's really hard to gauge what someone is experiencing by what they write online, because we only get your side of the story, and only one tiny sliver of it. So this is an honest question: Do you care about other people?
People don't offer friendship to people who just take take take, who just need to be with anyone who will take them in. I've become fast friends with people whom I've offered help. (I tend to overhelp, actually!) And those people are very generous with me back.
But it's hard to give when you have anxiety (or depression, for that matter). A hallmark of that is being focused on your own problems. It doesn't necessarily mean that you're a selfish person, but that's a selfish kind of behavior. If you're always focused on your own problems and what other people can do for you, it's hard for those other people to picture how you fit into
their lives in a way that's good for them and not just you.
You have to be comfortable with yourself first, before you get fight off the anxiety/depression enough to truly connect with others. But there are still ways you can start feeling connected and help get outside your own head, such as volunteering.
It can take a long time, and it will be something you have to work on continuously, but I've found that people who are anxious and focused on their own problems, tend to become very animated and come alive when they help others. It's very empowering.