Personally, I can't imagine wanting to die just because I'd been around for forever, but I know others feel differently.
The world-building here is excellent (if a bit playful), even if much of it is told rather than shown. The pixel-art style does a good job at taking a little bit of the edge off the subject matter (though your mileage may vary). The sideways view of death from immortals in a sci-fi setting does its job of being thought-provoking wonderfully.
It is, of course, quite melancholy (And maybe a bit controversial in it's characters' romanticisation of death. Again, I think it's doing a decent job as provocative speculative science fiction there. But definitely not something to read if you have issues with suicide), but it at least does a decent job at the "sweet" part of "bittersweet".
As an aside, whether or not this should have had a "tragedy" tag is... an interesting philosophical question, as to what is "tragic". It's probably a matter of one's perspective. But I think the subject-matter is probably sufficient warning for that much...? I'm not sure.
Having said all that, there are things in here that make me just a teeny tiny bit concerned that some of this is a cry for help on the part of the author. Not necessarily, but—especially given the similarly macabre themes of their other translated work—I hope they are well.