As for your point on the Qur'an, I have had a look at it, yes. It's arguably a lot less violent than the Old Testament, actually.
A few examples from the OT. You could argue that context matters (or that OT morality no longer applies since Christ), but you can argue similarly for the Qur’an.
1 Samuel 15:3
"Now go, attack the Amalekites and totally destroy all that belongs to them. Do not spare them; put to death men and women, children and infants, cattle and sheep, camels and donkeys."
https://www.biblegateway.com/passage/?search=1%20Samuel%2015%3A3&version=NIV
Numbers 31: 17–18
"Now kill all the boys. And kill every woman who has slept with a man, but save for yourselves every girl who has never slept with a man."
https://www.biblegateway.com/passage/?search=Numbers%2031%3A17-18&version=NIV
Psalm 137:9
"Happy is the one who seizes your infants
and dashes them against the rocks."
https://www.biblegateway.com/passage/?search=Psalm%20137%3A9&version=NIV
Bit violent, no? Now compare the Qur'an. Most of these also refer to specific battles and are not generic commands to attack non-believers.
Q2:191
"Kill them wherever you come upon them and drive them out of the places from which they have driven you out. For persecution is far worse than killing. And do not fight them at the Sacred Mosque unless they attack you there. If they do so, then fight them—that is the reward of the disbelievers."
https://quran.com/al-baqarah/191
Q9:5 [the famous “Sword Verse”]
"But once the Sacred Months have passed, kill the polytheists ˹who violated their treaties˺ wherever you find them, capture them, besiege them, and lie in wait for them on every way. But if they repent, perform prayers, and pay alms-tax, then set them free. Indeed, Allah is All-Forgiving, Most Merciful."
https://quran.com/en/at-tawbah/5
Q47:4
"So when you meet the disbelievers ˹in battle˺, strike ˹their˺ necks until you have thoroughly subdued them, then bind them firmly. Later ˹free them either as˺ an act of grace or by ransom until the war comes to an end. So will it be. Had Allah willed, He ˹Himself˺ could have inflicted punishment on them. But He does ˹this only to˺ test some of you by means of others. And those who are martyred in the cause of Allah, He will never render their deeds void."
https://quran.com/muhammad/4
If you argue that Muslims are taught to be violent from these verses, you can equally argue that Christians or Jews are taught the same from their own holy books.