I think this may be where some of the confusion on my part lies in reading what you said. Divinity or the Divine, does not necessarily mean related to a deity form. The Divine, which is a term I use extensively, which while used in reference God in traditional views of God as an "other", refers to not God as a person, but the essence of Ultimate or Absolute Reality, Absolute Purity, Goodness, Love, Truth, etc., (all of which are synonymous with divinity). It is is however beyond that. The Divine, or divinity, is state or condition of being. "The Divine in all things", for instance.You can also look to some dictionary definitions of mysticism to find the notion that divinity is a necessary component of a mystical experience. That is not what science has found, nor is divinity a key part of mysticism in some traditions.
For instance, Sri Aurobindo, who was absolutely a mystic of the highest order, extensively used that word. I have one of his books, which is a collection of his various teachings which is called The Life Divine. Here's an excerpt from it I saved because I quote from it all the time. You can see in it he uses Self, Truth, and the Divine, all interchangeably:
It is necessary, therefore, that advancing Knowledge should base herself on a clear, pure and disciplined intellect. It is necessary, too, that she should correct her errors sometimes by a return to the restraint of sensible fact, the concrete realities of the physical world. The touch of Earth is always reinvigorating to the son of Earth, even when he seeks a supraphysical Knowledge. It may even be said that the supraphysical can only be really mastered in its fullness – to its heights we can always search– when we keep our feet firmly on the physical. “Earth is His footing,” says the Upanishad whenever it images the Self that manifests in the universe. And it is certainly the fact the wider we extend and the surer we make our knowledge of the physical world, the wider and surer becomes our foundation for the higher knowledge, even for the highest, even for the Brahmavidya.
In emerging, therefore, out of the materialistic period of human Knowledge we must be careful that we do not rashly condemn what we are leaving or throw away even one tittle of its gains, before we can summon perceptions and powers that are well grasped and secure, to occupy their place. Rather we shall observe with respect and wonder the work that Atheism has done for the Divine and admire the services that Agnosticism has rendered in preparing the illimitable increase of knowledge. In our world error is continually the handmaid and pathfinder of Truth; for error is really a half-truth that stumbles because of its limitations; often it is Truth that wears a disguise in order to arrive unobserved near to its goal. Well, if it could always be, as it has been in the great period we are leaving, the faithful handmaid, severe, conscientious, clean-handed, luminous within its limits, a half-truth and not a reckless and presumptuous aberration."
Sri Aurobindo, The Life Divine, pg 13,14
In emerging, therefore, out of the materialistic period of human Knowledge we must be careful that we do not rashly condemn what we are leaving or throw away even one tittle of its gains, before we can summon perceptions and powers that are well grasped and secure, to occupy their place. Rather we shall observe with respect and wonder the work that Atheism has done for the Divine and admire the services that Agnosticism has rendered in preparing the illimitable increase of knowledge. In our world error is continually the handmaid and pathfinder of Truth; for error is really a half-truth that stumbles because of its limitations; often it is Truth that wears a disguise in order to arrive unobserved near to its goal. Well, if it could always be, as it has been in the great period we are leaving, the faithful handmaid, severe, conscientious, clean-handed, luminous within its limits, a half-truth and not a reckless and presumptuous aberration."
Sri Aurobindo, The Life Divine, pg 13,14
To say mysticism is the experience of the Divine, or that one experiences divinity, is not inaccurate. It is really simply a matter of what someone hears when they hear that term. And someone who has never experienced the Divine, or the Absolute, of Godhead, or Self, choose whichever word you prefer as they all point to the same thing, cannot understand the nature of what that actually is. So their understanding of those words are all perceived as something external to themselves, held in some "other" outside themselves because its origin is an idea or concept in their minds, rather than an understanding derived through experience that the Divine is what is in all things, and God is within, the Subject of one's own being, and not an object of beliefs. The Divine and Emptiness are to me synonymous terms.
Sorry if I'm a little prickly and defensive about these terms. Long ago I resolved to not give the power of these words, such as God or the Divine, away to the mythic-literal understanding of these words. They mean so very much more than how they are held in their minds. I think they are perfectly fine terms, and I don't like giving the power of them away by not using them or to somehow have to apologize for using them. The context in which they are used, what they are pointing to is what determines their position of strength. If someone says they sense the divine in their special crystals, whereas they don't recognize the divine in everything and everyone, this is obviously not what the mystic understands.