Jihad as per Quran

Jihad is mentioned in four places in the Qur'an as a noun, while its derived verb is used in twenty-four places. Mujahid, the active participle meaning "jihadist", is mentioned in two verses. In some of these mentions (see At-Tawbah 9/41, 44, 81, 86), it is understood that the word jihad directly refers to war, and in others, jihad is used in the sense of "the effort to live in accordance with Allah's will".

Source: https://en.wikipedia.org/wiki/Jihad#cite_note-Oz-28

The mentions according to the Hadiths would only hold as much value as a army officer's opinion on the necessity of war, when he mentions that to civilians.

Ibn Hazm (a Muslim polymath and philosopher) lists four kinds of jihad fi sabilillah (struggle in the cause of God):

• Jihad of the heart (jihad bil qalb/nafs) is concerned with combatting the devil and in the attempt to escape his persuasion to evil. This type of Jihad was regarded as the greater jihad (al-jihad al-akbar).
• Jihad by the tongue (jihad bil lisan) (also Jihad by the word, jihad al-qalam) is concerned with speaking the truth and spreading the word of Islam with one's tongue.
• Jihad by the hand (jihad bil yad) refers to choosing to do what is right and to combat injustice and what is wrong with action.
• Jihad by the sword (jihad bis saif) refers to qital fi sabilillah (armed fighting in the way of God, or holy war), the most common usage by Salafi Muslims and offshoots of the Muslim Brotherhood.

Meanwhile, the Islamic Golden Age saw the origin of a specific Hadith that's more rational:

A related hadith tradition that has "found its way into popular Muslim literature",[71] and which has been said to "embody the Muslim mindset" of the Islamic Golden Age "Abbasid Caliphate") (the period from the mid-8th century to mid-13th century following the relocation of the Abbasid capital from Damascus to Baghdad), is:

"The ink of the scholar is more holy than the blood of the martyr."