Suicide is a major sin. However it is not Kufr \ Shirk.
While the suicidee has done an act that deserves punishment, his fate is upon Allah and it is not necessary that he will go to Jahannum:
he can be forgiven through the mercy of Allah:
إن الله لا يغفر أن يشرك به ويغفر ما دون ذلك لمن يشاء
Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills.
— Quran 4:48
he can be forgiven because of intercession of the Prophet, angels, martyrs, righteous people etc.:
شفاعتي لأهل الكبائر من أمتي
My intercession will be for those of my people who have committed major sins.
— Sunan Abi Dawud
he may be punished, however this punishment will be finite and he will eventually be forgiven:
يخرج من النار من قال لا إله إلا الله وفي قلبه وزن شعيرة من خير
Whoever said "None has the right to be worshipped but Allah" and has in his heart good (faith) equal to the weight of a barley grain will be taken out of Hell.
As for the ahadith which warn of punishment for suicide. The have explained by the scholars as follows:
- They were specific to a certain non-muslim, not a general principle for all people.
- They apply to Kufr, i.e. one who does it while considering it to be lawful.
- They warn of what the rightful punishment is in order to admonish, however this will not necessarily be administered.
- They warn of a prolonged punishment, not an eternal one.
Refer to for example Fath al-Bari.
As for the case of a Muslim who commits suicide, there is hope that he may be forgiven without any punishment, among the evidence for which is the hadith on a suicide during the time of the Prophet:
أخذ مشاقص له، فقطع بها براجمه، فشخبت يداه حتى مات، فرآه الطفيل بن عمرو في منامه، فرآه وهيئته حسنة، ورآه مغطيا يديه، فقال له: ما صنع بك ربك؟ فقال: غفر لي بهجرتي إلى نبيه صلى الله عليه وسلم ... فقال رسول الله صلى الله عليه وسلم: اللهم وليديه فاغفر
So he took hold of an iron head of an arrow and cut his finger-joints. The blood streamed forth from his hands, till he died.
Tufail son of Amr saw him in a dream. His state was good and he saw him with his hands wrapped.
He (Tufail) said to him: What treatment did your Allah accord to you?
He replied. Allah granted me pardon for my migration to the Apostle (ﷺ).
The Messenger of Allah ﷺ said "O Allah, forgive his hands too."
Also see: Is it permissible to perform funeral prayers for someone who committed suicide?