The Buddhist approach is that being born as a human is the most favourable situation to reach awakening. Rebirth, is overwhelmingly likely to be into less favourable conditions - one metaphor is that to be reborn again as a human is as likely as a sea turtle in a whole ocean, coming up for air and doing so through a single small wooden hoop in all of that ocean.
Buddhist thought deconstructs the conventional self, and denies transmigration of an unchanging soul or identity, as illustrated in the candle metaphor from The Questions of King Melinda (quoted here Does Buddhism espouse reincarnation?). Who is reborn? Causes and conditions are reborn, only. Who are you? Do not answer with reference to the past or future.
Our core nature is pure awareness, in which sense we are all the same - when we are fully present. And the distinctions between ourselves and others is contingent, accidental, characterised by sunyata. We are not isolated separate individuals, but constituted by interbeing, like in the metaphor Indra's Net.
On the 'no harm' thesis about death, this answer in a discussion of it summarises some problems, which Buddhist thought also takes up https://philosophy.stackexchange.com/a/28525/30474 Viewed only from the individual subjectivity, death may not be a harm. But in the total picture it may or may not.
The Buddhist picture of harm is different, because it is about entanglements and karma, vs compassion, bodhicitta and letting go. Does the death create bitterness or resentment? That could be reborn. Does freely choosing death cultivate serenity, and embracing the larger view of one's life and the lives of others? That could result in fortunate rebirth. How death is experienced is crucial, and harms & benefits can continue. Because it's not truly that there is 'no person', but that boundaries between self, other, and world are challenged, and just as the self is understood to inherit karma such as embodied in language, so the consequences of their acts do not finish with their conventional death. Buddhism takes the middle path, between transmigration and materialism.
"There are those who do not realize that one day we all must die. But
those who do realize this settle their quarrels." - The Dhammapada