As a general note, since this seems to be a sort-of Mahāyāna-EBT contextualization and comparative thread, I should clarify on what at least I am able to from an informed perspective, with regards to some understandings of “interconnected/interpenetrating” that might be present, or perhaps better clarify some correct presumptions that were being made.
The tradition of Mahāyāna philosophy that I am most familiar with, and highly interested in, is, as Javi already pointed out, us knowing each other online already, the Tiāntāi school of China headed by Ven Zhìyǐ.
The Tiāntāi school of Buddhism is founded on what Ven Zhìyǐ referred to as “the integrated teaching”. Some would later call this “the Tiāntāi synthesis”.
Unlike how Mahāyāna (& Vajrayāna) entered into Tibet, and unlike how Indian Buddhism developed into its late complex stages in India, the entirety of the dispensations of the EBTs, the later sects, & Mahāyāna, all enter into China at more or less the same time, or at least in a very truncated timeframe as compared to the native development of Buddhism in the Indian subcontinent.
As a result, early Chinese Buddhists received these texts in more-or-less a freely distributed jumble, and often without commentarial material. For instance, over on DharmaWheel, Malcolm often says that the Tibetans learned their dharma from the commentaries, and the Chinese from the sūtras. How accurate he is in saying this I cannot say.
“The integrated teaching”, or “the Tiāntāi synthesis”, is, IMO, the logical outcome of how the Chinese inherited the dharma. If Ven Zhìyǐ had not undertook such a project, someone else would have. From the perspective of many here, understandably, they will see it as a pity that Ven Zhìyǐ incorporated some apocryphal (even by Mahāyāna standards) material into this synthesis. From that same perspective, it will be seen as unfortunate that Ven Zhìyǐ placed the Saddharmapuṇḍarīkasūtra as the definitive teaching of the Buddhas, rather than the āgamāḥ or something of the like.
As a result, there are some elements of the teaching that can reasonably be traced to earlier Buddhisms, and some that cannot be found explicitly stated in the dispensation to the śrāvakāḥ. For instance, this thread’s language, “Buddha-nature is the universe itself”, or “the universe is Buddha-nature”, is apparently rooted in the way that the thought of the Japanese people expresses itself in language.
National Teacher Enkan Saian in Kangshū Province was an esteemed Master under Baso. He once pointed out to his assembly, “All sentient beings are possessed of Buddha Nature.” Right away, we need to thoroughly examine his words ‘all sentient beings’. All sentient beings have different internal propensities and external conditions, which are the fruits of past karma, so their perspectives are different. This holds true for each and every one of them, be they called ‘ordinary people’, ‘non-Buddhists’, ‘those in the Three Courses’, ‘those in the Five Courses’, or something else. ‘All sentient beings’, as spoken of in the Buddha’s Way in the present instance, means that all who possess a mind filled with craving are ‘sentient beings’, since having a mind is synonymous with being a sentient being. All those whose mind is beyond craving will likewise be sentient beings, since being a sentient being is synonymous with having a mind. Accordingly, all minds are, without exception, sentient beings, and all sentient beings are, without exception, possessed of Buddha Nature. And even grasses, trees, and our very nation are synonymous with Mind, and because they are synonymous with Mind, they are sentient beings, and because they are sentient beings, they are possessed of Buddha Nature.
Or perhaps Ven Dōgen was being very "idiosyncratic" to assert what he asserted, even in the thought-realm of Japanese philosophy. Similar language of ‘this world is the Pure Land of the Buddha’ can also be found in Tiāntāi, and I am sure that a Zen teacher has said something similar in the past. What it means here is that the rock “is mind” (note, only Ven Dōgen AFAIK goes further and asserts the rock’s sentience on account of this) in the sense that it makes up the world that is within the mind. If sentience is understood as Buddha-nature, than the phenomenological realm of the ordinary mind is the Pure Land.
As such, interpenetration is solely one of emptiness, not appearance, from the perspective of the ordinary being, but also the non-Mahāyānist in general. In Tiāntāi, interpenetration is predicated on the relationship between appearance/aspect and emptiness. It is not that all appearances/aspects interpenetrate and are ‘one’, if I may refer back to the quote from Ven Zhìyǐ: “[when the first type of fool hears that ‘all dharmāḥ are empty’] they take it to mean that all dharmāḥ are inseparable from emptiness and that even if one were to traverse the entire universe, everywhere would be the same suchness [i.e. emptiness] as that found here as the suchness of, for example, this vase.” It should lastly be noted that there is a very small occurence of the word “interpenetration” found in all of the writings of Ven Zhìyǐ. “Interpenetration”, as applied here, is frequently a construct of Western academia.
On the subject of "interpenetration", it is 圓融. 圓 is etymologically (semantically technically) related to 圍 "to gird" and 國 "country", but in this sense means "encircling and" or "completely". 融 gets its semantic component from 鬲 “cauldron”. It means to intermix or fuse or melt into, referring to the way that things melt into each other (for instance in a cauldron during smelting specifically). Together 圓融 is "encircling and melted together" or "completely fused".
The main dictionary I consult gives this "interdependence / consumate interfusion / interpenetration", but that is rather vague. 'Consumate interfusion' seems to be a very popular translation for this, but it seems this is the model perhaps for the English 'interpenetration'.
From the more detailed Digital Dictionary of Buddhism we have:
Basic Meaning: consummate interfusion
Senses: Perfect interfusion; completely interpenetrated; seen more fully written as 圓滿融通 and 圓融無礙. Said of the ultimate reality as understood in Tiantai 天台 and Huayan 華嚴.
In Huayan, all existences are of themselves perfectly interfused. The absolute in the relative and vice versa; the identity of apparent contraries; perfect harmony among all differences, as in water and waves, affliction and enlightenment, transmigration and nirvāṇa, or life and death, etc.; all are of the same fundamental nature, all are thusness, and thusness is all; waves are one with waves, and water is one with water, and water and wave are one.
In Tiantai, the usage of the term is more in application to the nonobstruction among various approaches to the Buddhist doctrine, and thus we see terms such as perfect interfusion of the three disciplines 圓融三學, perfect interfusion of the three truths 圓融三諦, perfect interfusion of the unmoving 圓融無作 and so forth.
[Charles Muller, Robert Buswell; source(s): Ui, Nakamura, JEBD, Yokoi, Iwanami]
Perfect, complete (Skt. pariniṣpanna, paripūrṇa, pariṇāma). [Charles Muller; source(s): Hirakawa]
I am not sure if it is suggesting that 圓融 is an occasional Chinese translation choice for the Sanskrit pariniṣpanna, paripūrṇa, (et al) or not. Running a scan of the Taishō Tripiṭaka we see that 圓融 is a sparsely occuring word, with most of its instances limited to T09b–10 (the Avataṃsaka-Gaṇḍavyūha volume) & T44b–48 (Sarvasamaya, the sectarian teachings).
The oddball occurrence is in the Śuraṅgamasūtra. The rest are in minor apocryphal texts here and there.
Other than in those texts, the other place that it tends to occur is in commentarial material (like in T44b–48 like I already mentioned). Going down the list we have a bunch of commentaries, including two significant commentaries from the Tiāntāi school: Ven Zhìyǐ's 妙法蓮華經玄義 ('The Subtle Dharma of the Lotus Flower Sutra's Profound Meaning') & Ven Zhànrán's 法華玄義釋籤 ('The Dharma Flower's Profound Meaning Guidebook').
Ven Zhìyǐ uses it to refer to the Three Truths in the twice-above-mentioned commentary: 分別者，但法有 麁妙，若隔歷三諦，麁法也；圓融三諦，妙法也。
Interestingly, 圓融 is not a term in the Lotus Sūtra's material text, the textus receptus, as it were.
Ven Zhìyǐ himself was an East Asian Madhyamaka (a subschool of greater Madhyamaka), and his Buddhist education was generally in that milieu. Regardless of whether the above “works” with Ven Nāgārjuna’s exegeses of the empty, and by that I refer to the Nirvānaparīkṣā of Ven Nāgārjuna's Mūlamadhyamakakārikā****, looking at the world on terms of the relation between emptiness and appearance/aspect, this is a very fundamentally different philosophical angle than what undergirds Buddhadharma practice as explained and attested to in EBTs, the dispensation (exclusively) to the śrāvakāḥ.
That being said, this, what I present (not necessarily what I am presenting about), is all somewhat surface-level philosophizing, only my own understanding, and perhaps my own misconceptions. You wont find this kind of language or expression in any early Indian Buddhist text. But is it entirely unBuddhist? I do not think so.
****the abovementioned exegesis of the empty, Ven Nāgārjuna, Mūlamadhyamakakārikā:
(Siderits & Katsura translation, [additions mine])25:19-20
न संसारस्य निर्वाणात् किं चिद् अस्ति विशेषणं
na saṁsārasya nirvāṇāt kiṁ cid asti viśeṣaṇaṁ
There is nothing whatsoever of samsara distinguishing (it) from nirvana.
न निर्वाणस्य संसारात् किं चिद् अस्ति विशेषणं। १९
na nirvāṇasya saṁsārāt kiṁ cid asti viśeṣaṇaṁ| 19
There is nothing whatsoever of nirvana distinguishing it from samsara.
निर्वाणस्य च या कोटिः।कोटिः। संसरणस्य च
nirvāṇasya ca yā koṭiḥ koṭiḥ
[That which] is the limit which is the limit of nirvana [is the] the limit of samsara;
न तयोर् अन्तरं किंचित् सुसूक्ष्मम् अपि विद्यते। २०
na tayor antaraṁ kiñcit susūkśmam api vidyate| 20
Even a very subtle interval is not found of (between) them.