Is it permissible to eat meat not slaughtered according to Islamic law after mentioning the name of Allah over it, and is this the correct understanding of the Bukhari hadith that permits mentioning the name of Allah over meat whose permissibility is not confirmed?

If the method of slaughter is unknown, but there is a strong presumption that the animal was slaughtered according to Islamic law (because the slaughterer is a Muslim or from the People of the Book), then merely mentioning Allah's name (Tasmiyah) before eating is sufficient. However, if it is known that the slaughter was not performed according to Islamic law, then it is not permissible to eat from it, as it is considered carrion (maytah).