This is a tough situation, I really feel for you :(.
It's so hard to know what to do in situations like this, especially considering she is a long term best friend. Of course, the social signals she is putting out would make you feel like you should back away from the situation; however when dealing with depression, I think this is not the case.
Even if people are depressed and unresponsive, it is still important to reach out to them. They may be going through things that they wish to deal with alone (for the moment), however knowing that there are people out there that are still wanting to support you means a lot (Especially in the long-term) :)
Perhaps you can send her messages less frequently (like twice-week, whatever feels right), but I would not break contact completely. If she ever does feel like responding, be supportive rather than lecturing- listening to her, sympathise with her. You could mention getting help if the situation feels right, however due to (what sounds like) her stigma against seeking help, it might pay to be careful around this topic.
Even if she doesn't respond, I would still recommend checking in. Try to understand that the world is currently different from her point of view- try not to let it get you down if she doesn't respond or responds negatively.
Finally, I just want to check in with how you are feeling? Anxiety is difficult to manage in situations like these. If you want to talk about anything, you can do so here :)
I hope this has been somewhat helpful. Hopefully some more people can drop in to offer support or their own experiences/opinions. Keep in touch, if you feel like it! :)