If God determines absolutely everything, then the choice was determined. That means it's not an actual choice. … Nothing is voluntary if absolutely everything is determined by God.
This line of reasoning stands on a hidden premise—that a choice is only a choice if it is undetermined (or self-determined in a contra-causal sense). This simply begs the question against compatibilism which,
by definition, rejects that premise.
(This also makes a mess of moral responsibility. A will that is not determined by nature, reasons, or desires is not free in a meaningful sense; it is arbitrary. But that is a different nut to crack in a separate thread.)
Determined and choice are not mutually exclusive categories. This is about
unforced choice, not
uncaused choice. A determined event can still be a deliberate, intentional, desire-expressing act—because causal determination is not the same thing as coercion or compulsion.
“Does choice imply more than one actual possibility exists?”
Yes. The word “choice” literally means a selection can be made from two or more possibilities!
That word (possibilities) is exploiting an ambiguity that needs to be clarified. In ordinary language, choice presupposes that the agent considers more than one option—chocolate or strawberry, reason x or reason y, coffee or tea, call in sick or go to work. Those are
deliberative possibilities, objects of evaluation, intention, desire. Compatibilists fully affirm this category of possibility.
Your answer tacitly introduces a stronger claim, that choice entails
metaphysical possibilities (i.e., multiple metaphysically open outcomes) in the moment. That does not follow from the ordinary meaning of the word choice—i.e., that isn’t what it “literally” means. It is a philosophical add-on. Lexically, choice means something like “the act of selecting or deciding.” It doesn’t encode a causal theory or modal metaphysics, and dictionaries don’t define choice as requiring indeterminism or multiple causally open futures.
Choice requires deliberative possibilities, not metaphysical possibilities.
At the moment of choice, only one outcome is actualizable, given the total state of affairs and God’s eternal decree. Nevertheless, a range of outcomes is possible
relative to the agent’s deliberative perspective—“If I choose P, then x will occur; if I choose ¬P, then ¬x will occur.” This conditional structure—grounded in the agent’s reasons, intentions, desires, and volition—is sufficient for genuine choosing and for moral significance. And it doesn’t require denying determinism.