The question of whether God forgives addiction is not usually a theological question. It is a personal one. It is the person who has relapsed again asking whether they have finally used up whatever was left. It is the person who has been sober for three years but cannot shake the feeling that what they did inside the addiction placed them in a category God doesn't cover. It is the person who grew up in the church and knows the Sunday school answer and cannot feel it as true for themselves.
Addiction is one of the wounds where the lie that you are the exception is most convincing. Every other person, God forgives. This is different. This is too many times. This is too much damage. This is something you chose, over and over, even when you knew what it was doing. That reasoning feels airtight from the inside. It is not true.
1 John 1:9 says God is faithful and just to forgive when we confess. Romans 8:1 says there is no condemnation for those who are in Christ Jesus. Neither of those promises has an asterisk for addiction, for relapse, for the number of times, for the severity of the damage. The promise is the promise.
That is a different kind of hard. The theological answer is available. The felt experience of it — the actual sense that you are covered, that you are not the exception, that the distance between who you have been and who God is has been crossed — that takes longer. And it cannot be argued into existence. It has to be received somewhere quiet, over time, in a place where the question is allowed to stay a question without being rushed.
Romans 7:15 — "I do not understand what I do. For what I want to do I do not do, but what I hate I do" — was written by someone who understood what it means to be a person in conflict with their own behavior. That is not a verse about addiction specifically. It is a verse about the human experience of doing the thing you do not want to do, again. That experience is not foreign to God. It is named in scripture by someone who knew it firsthand.