Does the statement, "By God, I will not play with this weapon again," constitute a binding oath (yamin mun'aqidah) or a vain/unintended oath (laghw), knowing that the speaker returned to playing with it, and the matter recurred with another weapon?

The mentioned oaths are binding oaths because they pertain to a future event, and are not considered a "vain oath" (laghw al-yamin). For expiation (kaffara) to be obligatory, the oath must be binding, meaning it is possible to either fulfill or break it, and it must refer to the future. As for an oath concerning the past, it is not binding and is of two types: a ghamus oath (sworn by a liar who knows they are lying, considered a grave sin for which there is no expiation), and a vain oath (laghw al-yamin) which is uttered unintentionally, such as saying "No, by Allah" or "Yes, by Allah" during conversation. If someone swears an oath concerning a past event, believing themselves to be truthful, but it turns out to be otherwise, they are only considered to have broken the oath in matters of divorce and manumission, not in oaths sworn by Allah or vows.