Is it considered perjury and does it necessitate expiation for an oath (kaffarat yamin) if a person swore an oath during Friday prayer to abandon a sin, with a heartfelt intention and partial utterance, then returned to that sin?

An oath is not contracted except by uttering the words of the oath and the thing sworn upon; it is not by intention alone. If you utter the words of an oath and intend to abandon a sin, your oath is not complete, and therefore there is no expiation upon you for returning to the sin. We warn you against falling into sins. If you intentionally swear during Friday prayer, your prayer is invalid, and you must make it up as Dhuhr. However, if the swearing was out of ignorance or forgetfulness, there is a difference of opinion regarding the validity of your prayer, and it is safer to make it up as Dhuhr to avoid disagreement.