Hello.
What you are worried about comes through, but it seems necessary to sort out a little bit about what the Buddha thought.
The Buddha discovered that the more self-centered work (suffering) of trying to make reality the way you want it, the more it struggles to diverge from reality. To put it bluntly, they try to do what they want and it doesn't turn out the way they want; this is the cause of suffering.
It is exactly true when it comes to four struggles and eight hardships.
Here, we only touch on life, old age, illness, and death (four tribulations), but even though I want to stay young forever, I have to get old; I don't want to get sick but I have to die even though I don't want to die. Also, being born into that reality and being forced to do so is the famous birth and old age illness and death (life is born).
Since you were taught that “Buddha's fear of death is due to an obsession with life,” you seem to understand that “taking your own life is not a bad thing,” but “it should be tolerated.”
There seems to be some confusion in language and way of understanding, but the Buddha faced his own heart (anguish) of not being able to accept the reality that he would always die. I made the choice to face myself. It's not a choice to “take your own life.”
Meanwhile, you wrote, “I'm heartbroken, my job isn't going well, I don't like myself, and I want to die even more.” In other words, this means they say “I want to die” because they try to make reality the way they want it and it doesn't turn out the way they want, and it seems like a state where they are unaware of the function of one's heart (worry) itself in the first place. In other words, at this stage, the direction is different from how to deal with death with the Buddha, and there is a difference in understanding.
If you change your point of view, it can also be said that you are about to stand at the starting line where the Buddha was noticed. By all means, sit back and learn the teachings of a purpose you have a connection with. Once you have studied the introductory book properly, it will be quite different.
I hope that the Buddhist relationship will deepen in the future.
appending
I hope it helps.
Please ask questions if you have a relationship again.
Let's spit out more and more without worrying about it alone.
Take care.