Are those considered martyrs without being killed in combat subject to ritual washing and funeral prayer?

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Martyrs who die due to ailments such as abdominal pain (battun), plague (ta'un), drowning, collapse of a structure (hadm), or post-natal bleeding (nifas) must undergo ritual washing (ghusl) and have the funeral prayer (Salat al-Janazah) performed over them. This is the established ruling concerning them. Evidence supports this practice: The Prophet, peace be upon him, prayed over a woman who died in her nifas, standing in the middle of her. Furthermore, the Prophet prayed over Sa'd ibn Mu'adh, who was a martyr. The Companions also prayed over Umar and Ali, both of whom are considered martyrs. The Prophet enumerated five categories of martyrs: the plague victim, the one with abdominal pain, the drowned, the victim of a building collapse, and the martyr in the cause of Allah, a narration deemed Hasan Sahih by Al-Tirmidhi. Another narration adds seven categories beyond direct killing: the victim of fire, the victim of pleurisy (dhat al-janb), and a woman dying while still a virgin (tamutu bi-jam'), all of whom are washed and prayed over.