What is the meaning of "a ray of light which illuminates thousands of buddha fields in the east" in the Mahayana Lotus Sutra?

When the Buddha of the Mahayana illuminates the sāhasracūḍikalokadhātu (thousandfold world-system), it is not the first time that he does this. He did this before when he preached the first of the sūtras that comprise the Mahāprajñāpāramitā vaipulya, also before when he preached the Buddhāvataṃsakasūtra. I hope this is not too long, moderation can inform me if it is, but this is from the publicly-available Mahāprajñāpāramitopadeśa translated by Venerable Migme Chödrön. In it, the commentary discusses why the Buddha is said to have emitted light when he taught the Prajñāpāramitā. He similarly lit the world in the depiction in the Lotus Sūtra:

Sūtra: From these rays (raśmi) came a great light (avabhāsa) that illuminated (parisphoṭati) the trisāhasramahāsāhasralokadhātu. From the trisāhasramahāsāhasralokadhātu, it went to illuminate universes in the east (pūrvasyāṃ diśi) as numerous as the sands of the Ganges (gaṅgānudīvālukopamā lokadhātavaḥ). And it was the same in the south (dakṣiṇasyaṃ diśi), in the west (paścimāyāṃ diśi) and in the north (uttarasyāṃ diśi), in the four intermediate directions (vidikṣu), at the zenith (upariṣṭhād diśi) and at the nadir (adhastād diśi). (see notes on the Ten Directions) And all the beings touched by this light were settled into supreme perfect enlightenment (ye ca sattvās tena mahatā raśmyavabhāsena sphutā avabhāsitās te sarve niyatā abhūvan anuttarāyāṃ samyaksaṃbodhau). [113c]

Question. – The nature of fire (tejas) is flame which rises upward (ūrdhvajvāla), that of water (āpas) is moisture which tends to go downward (adhaḥsnigdhatā), that of wind (vāyu) is sinuous movement (tiryaggamana). Therefore the vapor ignited by the rays [of the Buddha] will necessarily go upwards. Why does the sūtra say that that it illuminates everywhere (parisphoṭati) the trisāhasramahāsāsralokadhātu and the universes of the ten directions?

Answer. – The rays are twofold: vapor of fire and vapor of water; such are the vapor of fire of the sun-stone (sūryakānta) and the vapor of water of the moon-stone (candrakānta).1 Although the nature of fire (tejolakṣaṇa) is to blaze upward, the fire in the human body rises, descends and penetrates everywhere. It is the same for the solar fire and it is in this way that the waters of the earth dry up in the summer months. Thus we know that fire does not always rise upward.

Furthermore, by the power of the Buddha, these rays penetrate the ten directions like an arrow (iṣu) shot by a bow (dhaṇus) goes straight to the target.

Question. – Why do these rays first light up the east and only after that the south, the west and the north?

Answer. – Since the sun rises in the east, the east is first; the Buddha, who is in harmony with people’s ideas (sattvacittānuvartanāt), lights up the east first. Furthermore, we will always come up with the same difficulty: if he first illuminated the south, we would wonder why he did not first illuminate the east, the west and the north; if he illuminated first the west or the north, the difficulty would be the same.

Question. – When do the rays disappear?

Answer. – The Buddha uses his miraculous power (ṛddhibala); as long as he maintains it, the rays persist; when he lets it go, the rays disappear. The Buddha’s rays are like a lamp (dīpa) and his miraculous power is like the oil (meda); as long as the Buddha does not abandon his miraculous power, the rays do not disappear.

[...]

Sūtra: Then by means of his usual light (prakṛtiprabhā) the Bhagavat illumined the trisāhasramahāsāhasralokadhātu; this brilliance extended to all the universes of the east as numerous as the sands of the Ganges, and it was the same in the ten directions. All the beings who were touched by this light were destined to supreme complete enlightenment (Atha khalu Bhagavān prakṛtiprabhayā trisāhasramahāsāhasraṃ lokadhātum avabhāsayāmāsa. yāvat pūrvasyāṃ diśi gaṅgānadīvālukopamā lokadhātavas tayā prabhayā avabhāsitā abhūvan. yāvat daśasu dikṣu gaṅgānadīvālukopamā lokadhātvas tayā prabhayā avabhāsitā abhūvan. ye ca sattvas tayā prabhayā spṛṣṭās te sarve niyatā abhūvan anuttarāyāṃ samyaksaṃbodhau).

Śāstra: First the Buddha smiled with his entire body (sarvakāyāti) then he emitted rays from the pores of his skin (romakūpebhyaḥ); why now does he exhibit his usual light (prakṛtiprabhā) to light up the ten directions?

Answer. – Some people who have seen the different rays [shooting out from the body and the pores of the Buddha] believed that this was not the light of the Buddha. [Now] seeing the great development of the usual light of the Buddha, they are filled with joy (muditā) and, recognizing the true light of the Buddha, they finally reach anuttarasamyaksaṃbodhi.

Question. – What is the usual light (prakṛtiprabhā) of the Buddha?

Answer. – It is a light one armspan in width (vyāmaprabhā) surrounding the body of the Buddha on all sides; the Bodhisattva possessed it since his birth and it is one of the thirty-two marks (lakṣaṇa) called vyāmaprabhālakṣaṇa. (see Appendix 3)

Question. – Why is the usual light of the Buddha one armspan in width (vyāma) and not larger?

Answer. – The usual light of the Buddha is immense (apramāṇa) and lights up the universes of the ten directions. The miraculous bodily light of the Buddha Śākyamuni is immense; it is the width of one armspan, a hundred armspans, a thousand prabhedakoṭi of armspans and fills up the trisāhasramahāsāhasralokadhātu and the ten directions. However, the Buddhas’ custom is to manifest in the world of the five corruptions (pañcakaṣāyaloka), where beings are of middling qualities (guṇa) and knowledge (jñāna), a brilliance of only one armspan (vyāmaprabhā). If he showed a larger brilliance, the people today, of little merit (alpapuṇya) and weak faculties (mṛdvindriya), would be unable to tolerate the light. When a person sees a god, his eyes are blinded because the greater the [outer] light, the more the eye contracts. It is to people of keen faculties (tīkṣnendriya) and eminent merit (gurupuṇya) that the Buddha shows his immense brilliance (apamāṇaprabhā).

Besides, there are people who, seeing the usual light of the Buddha, rejoice (pramodante) and find salvation.

In the commentary, the light is described as related to the halo/aura of the Buddha. The halo of the Buddha appears in even the "Early Buddhist Texts." It appears in Saṃyuktāgama Sūtra No. 197 and in Venerable Buddhaghosa's commentary on the Dhammasaṅgaṇī, a Pāli Abhidharma text, and in Pi Tv Kd 1 in the Pāli vinaya.

In the Lotus Sūtra, the halo of the Buddha, the rays of light, illuminate the pure lands of the Buddhas. This is related to the idea in the Lotus Sūtra that world-systems are also kinds of pure lands ruled by their Buddha. In the Brahmājālabodhisattvaśīlasūtra, Vairocana Buddha dwells in the pure land of the Lotus Vault surrounded by world-systems, each replete with an emanated Śākyamuni Buddha with his pure land. In Chapter 16 of the Lotus Sūtra, Śākyamuni Buddha enigmatically declares "this land" as his pure land, and declares that it is always tranquil, even when living beings witness it destroyed by fire at the end of the world.