Thank you for the interesting question!
As you know, there are a number of differences between the Qur'anic and Biblical stories of similar people. Muslims and those who believe in a literal interpretation of the Old Testament will have to agree to disagree until the day comes when the truth is made clear!
In this case, it is more complicated because it is not 100% clear that Talut is the same person as Saul because they have different names.
There is a good discussion of the story in the relevant section of The Study Quran, ed. S. H. Nasr. Also here are some hadith on the subject. https://www.al-islam.org/hayat-al-qulub-vol-1-allamah-muhammad-baqir-al-majlisi/account-ishmaeil-talut-and-jalut