Bukhari

Hadith Commentary:
Some individuals have deduced from this hadith that reciting "Bismillah" over the slaughtered animal is not obligatory, because if it were obligatory, the Messenger of Allah (sallallahu alayhi wa sallam) would not have permitted the Companions (radi Allahu anhum) to eat the meat. However, this deduction is not correct, because although the Bedouins had only recently entered Islam, they were not ignorant of reciting "Bismillah."
It is quite possible that they used to slaughter while reciting "Bismillah," but the Companions (radi Allahu anhum) expressed doubt about them, thinking perhaps they did not recite "Bismillah." So the Messenger of Allah (sallallahu alayhi wa sallam) removed their doubt, stating that one should have a good opinion regarding a Muslim.
When they are Muslims, then certainly they would recite "Bismillah." However, to remove your own doubt, you should recite "Bismillah" yourselves.
In this regard, a hadith is also presented:
"The slaughter of a Muslim is lawful, whether he mentions the name of Allah or not."
But this narration is weak in terms of its chain of transmission.
(Irwa’ al-Ghalil: 8/169, no. 2537, and Fath al-Bari: 9/787)

Takhrij:
«أخرجه البخاري، الذبائح، باب ذبيحة الأعراب ونحوهم، حديث:5507.»©Explanation:
➊ From this hadith, it is understood that unless it is definitively and certainly known about a slaughtered animal that the name of Allah was not mentioned over it and that it is unlawful, one should not declare it unlawful merely on the basis of doubts—especially when the slaughtered animal belongs to a Muslim brother.

➋ Regarding the People of the Book (Ahl al-Kitab), if it is certain that he mentioned the name of Allah while slaughtering—for example, one witnessed the slaughter himself or a trustworthy Muslim witnessed it—then the animal slaughtered by such a person from the People of the Book is also permissible.

The slaughtered animal of other non-Muslims is not permissible.

And Allah knows best.