Am I being emotionally manipulated?

[TW, suicide threats.]

There's this person I know who constantly says they're depressed and suicidal. They're part of this friend group who I know would support them should they reach out to them, yet they only reach out to me. They're extremely emotionally sensitive and will think worst-case scenarios if I don't respond soon enough, have enough free time for them, or say something that unintentionally hurts their feelings.

Recently, they have been threatening suicide. For a few days consecutively they keep changing their bio to read stuff like "Thank you," and "I may be dead or alive." I keep thinking, "Don't assume they're crying wolf," or otherwise trying to get concern out of me by threatening suicide. Because even though it feels like they're crying wolf, I have to treat every threat as a cry for help. I message them, console them, try to keep them safe, then later they change their bio to normal. But only after I talked to them.

Now a few hours ago I got upset and didn't want to talk to them. So in response they did it again, claim that they "may be dead or alive." A few hours later they messaged me, so I know at the time they were still alive. And I honestly believe they still are.

Since I'm the only one this person essentially reaches out to, I feel so compelled to be available 24/7 for them. I have to be emotionally available and comforting all the time. But at this point they are draining me. I'm exhausted and stressed. Sometimes they trauma dump on me or will mention triggering things, but I can't tell them to stop because they'll just feel devastated and threaten suicide again. I am, at this point, emotionally exhausted. I don't want to assume it's for attention. I hate that I'm really starting to feel like it is.