This is a very long article in the Stanford Encyclopedia of Philosophy on Tiantai Buddhism that is quite thorough and good: https://plato.stanford.edu/entries/buddhism-tiantai/
It showed me that the whole concept of the Buddhanature of insentient beings is soemthing more of a rhetorical device or a logical trick to that further illustrates true insight being beyond dualistic discriminations (or descriptive language for that matter). For each argument, there is an inversion that is equally valid yet seemingly diametrically opposed. It is less a radical doctrine, and more an encouragement to remain mindful of the great complexity of conditioned relationships composing the emptiness experienced as realms and beings.
The controversial idea of “the Buddha-nature of insentient beings” is developed by Zhanran in his Jingangpi using a slightly different approach to the Three Truths, focusing on the trope of space as advanced as a metaphor for Buddha-nature in the Mahāyāna Nirvana Sutra, in its character of all-pervasiveness, ineradicability, and indivisibility, and the non-different/non-identical relation of all regions of space to each other and of each region of space to whatever possible object can occupy it. But here too the central argument is the inseparable intersubsumption of the two opposite terms: sentience is always insentience-sentience, insentience is always sentience-insentience.
One way to think about this is to consider a magnet. It has a north and a south “pole” to it. If we wanted to separate the north from the south pole, we might try cutting it in half. But when we do so, we find that each half still has both a north and a south pole. No matter how many times we slice it, the total set of different characteristics pertaining to the whole are also found in that separate part: northness and southness are, in their entirety, found in what was formerly, in the context of the whole magnet, purely the north part, and also in the former south part. This is how it is in the Tiantai universe: the universe is one big magnet, but instead of just a north and a south, it has 3000 different characteristic aspects: meness, youness, trains, oceans, dogs, soups, historical incidents, smiles, tears, delusion, enlightenment. If we try to isolate any of these, however, what we end up with is another entire “magnet”, which also has all 3000 aspects to it: this meness, it turns out, also has its youness part, its train part, its ocean part, its dog part, and so on. When I face you, it is you-and-me facing you-and-me. It is me-and-all-worlds facing all-worlds-and-me. It is the entire universe facing the entire universe. We are always different, because wherever we go, there is a you and a me, two different aspects, never merging into a blank indifferent mush of a single quality. But since me-and-you is contrasted to me-and-you, there is really no contrast at all: the same thing is found on both sides of the contrast. We are neither the same nor different. We are divided from ourselves, impossible to unify into a simple unity, but for that very reason we are impossible to separate from one another. Each of us, at each moment, are, in a word, absolute, the Center as which all appears, and which is appearing in and as all things. All things are our transformation bodies, we are the transformation body of all things.