How do Buddhist schools reconcile ‘non-arising of new karma’ with continued functioning of the aggregates between sopadhiśeṣa-nirvāṇa & parinirvāṇa?

Across early Buddhist and later scholastic sources, sopadhiśeṣa-nirvāṇa refers to the awakening of an arahant/Buddha during life, while the five aggregates continue to function. Parinirvāṇa (or nirupadhiśeṣa-nirvāṇa) designates the complete cessation of the aggregates at death. However they raise several questions - If the liberated mind is already free of defilements at sopadhiśeṣa-nirvāṇa, what exactly “continues” until parinirvāṇa? Is it- - merely biological life-supporting karma? - non-karmic causal processes of the aggregates? - a conventional designation with no metaphysical content? - or something else depending on doctrinal school? Furthermore, 1. What specific causal theory does each major tradition (Theravāda, Sarvāstivāda, Yogācāra, Madhyamaka) use to explain why the aggregates continue to arise after sopadhiśeṣa-nirvāṇa? 2. If the arahant produces no new karma, what prevents the aggregates from ceasing immediately at awakening? 3. Do any schools argue that the distinction between sopadhiśeṣa-nirvāṇa and parinirvāṇa is ultimately conventional rather than reflecting two ontologically distinct states?