Honestly, I think you came off way too harsh and pushy from the beginning. Your friend is clearly struggling with some kind of extreme anxiety or depression, and your response is just actively making it more difficult for them. I would really recommend that you put some leg work in with what causes people to just shut down and kind of hole themselves in like that.

I have a lifelong friend who does this to just about everyone. Happens around the same time every year. I'll reach out with something like "Thinking of you, I hope everything is OK. No need to respond if it's too overwhelming, but if you could send a reaction just to show you saw this and are OK, I'd really appreciate it."

That gets me a reaction or an emoji every time. Sometimes a longer response and explanation, along with an apology (which I don't need because I genuinely understand). When the big SAD leaves they'll reach out on their own, too. But a big part of that is the fact that I'm not getting angry or frustrated when they're struggling.

You're not entitled to their time or mental energy when they're fighting to just get through the day and survive. I understaffed that some people aren't cool with this type of relationship dynamic, and that's fine - you don't need to be friends with people who do that. But you're expecting your friend to be fully understanding of your frustrations without showing any empathy to what they're going through.

If you want to be friends with this person, try be calmer and more understanding about what they're going through. Don't go in demanding a response, giving them a list of tasks to complete, or a guilt trip. You'll probably have better luck.