Concepts
लोकसंग्रहः
lokasaṅgrahaḥ
loka 'world, people' + saṁgraha 'holding together' — the holding-together of the world. Krishna's stated reason (3.20) why the one who needs nothing still acts.
If liberation is the point, why would the liberated keep working? Krishna's answer names King Janaka — realized, and ruling — and adds a reason that has nothing to do with self-interest: people walk the path the best among them walk. The commentators differ on what the wise one's action IS, but none allows retirement from the world as wisdom's proof.
Janaka attained perfection through action alone
कर्मणैव हि
संसिद्धिमास्थिता जनकादयः
It is through action (without attachment) alone that Janaka and other wise men reached perfection. Having an eye to maintenance of the world order too you should take to…
what the best does, the world follows
यद्यदाचरति
श्रेष्ठस्तत्तदेवेतरो जनः
For whatever a great man does, that very thing other men also do; whatever standard he sets up; the generality of men follow the same.
act as the wise do — unattached, for the world
सक्ताः कर्मण्यविद्वांसो
यथा कुर्वन्ति भारत
Arjuna, as the unwise act with attachment, so should the wise man, seeking maintenance of the world order, act without attachment.
Because people follow what you do, not what you say — and because being finished with your own needs doesn't finish your obligations. Janaka ruled a kingdom after realization, and Krishna points at him: like that (3.20). Śaṅkara adds that the wise keep working so the world holds together; Jñāneśvar, that whatever the elders do becomes everyone's dharma by morning. If your wisdom makes you useless to the people around you, the Gītā does not call it wisdom.
Ādi Śaṅkarācārya · Advaita
Śaṅkara reads Janaka both ways — realized, he acted on by prārabdha for the world's cohesion; unrealized, action was his purification — and either way the duty to act stands.
लोकसङ्ग्रहार्थं प्रारब्धकर्मत्वात् कर्मणा सहैव असन्न्यस्यैव कर्म संसिद्धिमास्थिताः — for the holding-together of the world, their karma already in motion, they reached perfection with action itself, without renouncing it.
Śaṅkara Bhāṣya on 3.20 (Sanskrit, GitaDeep corpus; working rendering under review)
Śrī Rāmānuja · Viśiṣṭādvaita
For Rāmānuja the wise one's continued work is altruism in the strict sense — action whose beneficiary is the world.
So understanding that the whole Earth benefits from the performance of prescribed Vedic activities, one should act altruistically not for themselves but for the welfare of the world.
Gītā-bhāṣya on 3.21 — English translation (GitaDeep corpus)
Śrī Jñāneśvar · Vārkarī
The Jñāneśvarī grounds it in how norms actually propagate: what the elders do becomes the dharma others live.
Whatever the elders do, is called the religion and it is followed by others (ordinary persons). This is just in accordance with the order of nature and therefore especially the saints of higher insight should continue doing their duties according to their own religion without hesitation.
Jñāneśvarī on 3.21, tr. R. K. Bhagwat (GitaDeep corpus)
Swami Ramsukhdas · Sādhak Sañjīvanī
The practice reading keeps Janaka concrete: a householder's life, lived to liberation through action.
some great souls like Janaka, before and after him, leading householder's life attained salvation by action.
Sādhak Sañjīvanī on 3.20 — English translation (GitaDeep corpus)
Where the traditions differ, we show the difference.