What is the ruling on the prayer of one who clears their throat, laughs, or cries during it, and does a little speech invalidate the prayer?

Scholars differ on the ruling concerning clearing one's throat during prayer:

Case One: If clearing one's throat is due to necessity or an overwhelming urge: Generally, it does not invalidate the prayer according to scholars, and the worshiper is excused.

Case Two: If clearing one's throat is voluntary and without necessity:

Shafi'is: They hold three differing opinions: The soundest opinion: The prayer is invalidated if two letters become audible; otherwise, it is not. The second opinion: It does not invalidate the prayer even if two letters become audible. The third opinion: If the mouth is closed, it does not invalidate the prayer; otherwise, it is invalidated if two letters become audible.

Hanbalis: The prayer is invalidated if two or more letters become audible from it. However, Ibn Qudamah holds that it does not invalidate the prayer because it is not considered speech and is sometimes necessary, citing the action of Imam Ahmad and a narration from Ali (may Allah be pleased with him) as evidence.

Malikis: The prayer is not invalidated if there is a need for it, even if that need is not related to the prayer itself. However, if it is done playfully, the prayer is invalidated.