I agree with the rest of your replies, but I am very confused about these two quotes of yours:
Aren’t “the energies of the Holy Spirit” themselves part of “the very divine nature of God,” though of course they are not His essence, which is utterly impenetrable?
Yes, that would be technical imprecision on my part. Any energy ascribed to the Spirit belongs also to the Father and to the Son.
If not, in what way do we “partake of the divine nature” as Scripture says, if the energies we can partake of are not themselves God’s divine nature?
This question maybe requires a bit more attention, because the divine nature and the divine energies are related but not the same. Now, we have to be careful not to ascribe ‘parts’ to God, because God himself is simple and without parts. St. John of Damascus writes:The Deity is simple and uncompound. But that which is composed of many and different elements is compound. If, then, we should speak of the qualities of being uncreate and without beginning and incorporeal and immortal and everlasting and good and creative and so forth as essential differences in the case of God, that which is composed of so many qualities will not be simple but must be compound. But this is impious in the extreme. Each then of the affirmations about God should be thought of as signifying not what He is in essence, but either something that it is impossible to make plain, or some relation to some of those things which are contrasts or some of those things that follow the nature, or an energy.
Exact Exposition on the Orthodox Faith 1.9So when we make an apophatic statement, like that God is uncreated, we do not mean to say that uncreatedness is what He is in essence, but we mean that he is uncreated only in relation to us, who by contrast are created. When we say that God is incorporeal, we do not mean to say that what He is is incorporeity, but that He is not corporeal, unlike us. When we affirm cataphatic statements about God, like God is good or God is creative, we are not describing what his essence is, but we are describing either those things, “that follow the nature or an energy.”
So what is the relationship between a nature, what follows a nature and energy? For this, we can pull together a few other passages also from St. John of Damascus:Uncreate, without beginning, immortal, infinite, eternal, immaterial , good, creative, just, enlightening, immutable, passionless, uncircumscribed, immeasurable, unlimited, undefined, unseen, unthinkable, wanting in nothing, being His own rule and authority, all-ruling, life-giving, omnipotent, of infinite power, containing and maintaining the universe and making provision for all: all these and such like attributes the Deity possesses by nature, not having received them from elsewhere, but Himself imparting all good to His own creations according to the capacity of each.
Exact Exposition on the Orthodox Faith 1.14These properties belong to God by nature. In some sense, they follow nature, because anything of the divine nature will necessarily have all of these properties, not receiving them from any outside source, just as fire by nature has the property of heat, such that anything of the nature of fire must display heat. The Son and Holy Spirit, for example, possess all of the natural properties of the Father (this is opposed to his hypostatic property, which is causality) not through any form of participation, but by their very shared nature. Now what is energy? St. John of Damascus answers:All the faculties we have already discussed, both those of knowledge and those of life, both the natural and the artificial, are, it is to be noted, called energies. For energy is the natural force and activity of each essence: or again, natural energy is the activity innate in every essence: and so, clearly, things that have the same essence have also the same energy, and things that have different natures have also different energies. For no essence can be devoid of natural energy.
Exact Exposition on the Orthodox Faith 2.23And“For I live,” says the Lord, “and I shall glorify those who glorify me,” (1 Kgd 2:30) and the divine apostle, “So you are no longer a slave, but a son, and if a son, an heir of God through Christ,” (Gal 4:7) and “if we suffer together [with him], so that we are glorified together.” (Rom 8:17) You are not waging a war against images, but against the saints. John the theologian, who leant on Christ’s breast, there-fore says, that “we shall be like him.” (1 Jn 3:2) For just as iron plunged in fire does not become fire by nature, but by union and burning and participation, so what is deified does not become God by nature, but by participation. I am not speaking of the flesh of the incarnate Son of God; for that is called God immutably by hypostatic union and participation in the divine nature, not anointed by the energy of God as with each of the prophets, but by the presence of the the whole of the one who anoints. Because by deification the saints are gods, it is said that “God stands in the company of gods, in the midst he discriminates between the gods,” (Ps. 81:1) when God stands in the midst of the gods, distinguishing their several worth, as Gregory the Theologian interprets it.
Apologetic Treatises against those Decrying the Holy Images 2.19
By energy these properties which belong to God by nature are given to us by grace. Just like an iron through fire, becomes fire not by nature but by participation, we become gods not by nature but by participation. That is what it means when we are told that we will become partakers of the divine nature, even though we do not believe that the divine nature can be communicated to us.