[After a brain blast while talking to @perditos, I think I've maybe decided on what led to Halsin finally seeing he had a problem with alcohol and what made him basically quit drinking outright.
I think I mentioned before that his issues with drinking began after his imprisonment in the Underdark, but it worsened by far after the Shadow Curse was unleashed. However, I did not know what prompted him to quit drinking basically all together, but now I think I have an idea.
We know from his dialogue in the game that he found comfort in drinking alone at this point, and the Shadow Curse, his guilt, how he felt alone after losing his mentor and people he considered friends, and the new burden of Archdruidship all accelerated the amount he was drinking. It was something, if not the, one thing he felt he had control of, even though it was clear that the opposite was true. Therefore, he did not realize it had actually become a problem for quite some time. He did not see it affecting his leadership or disrupting his powers, so he did not feel the need to curb his drinking in any capacity.
I haven't decided on the finer details, but I think what ultimately does make him face the truth of his alcoholism is that it only made his depression to the point where he essentially and drunkenly denounced Silvanus and all his teachings. He got to the point where, in his frustration and anger with with the Shadow Curse, with his lack of progress in finding Thaniel or lifting it, in how alone he felt in his position as Archdruid that disallowed him from forming or reforming close bonds with others, he felt abandoned. By those around him, from the other druids, the Harpers, and Selunites, to his own god who he devoted the last few centuries of his life to. In this moment, Silvanus does step in and he cuts Halsin off. He loses his connection to nature entirely in an instant and it actually terrifies him. He cannot feel the plants and trees growing around him, cannot hear the voices of the animals around him, cannot access his Wild Shape.
If he felt lost and alone before, he certainly did in that moment. And, drunk as he was, he raged at first. All of that fear, sadness, and anger culminated into him taking that out on nature itself, leaving a swath of wreckage and violence unlike him in his wake. When he wore himself out just before sunrise, he fell to the ground and wept until his eyes burned and his throat was so raw he could no longer utter a word to express his rage and pain.
And, while time lessened the alcohol haze on his mind, nothing sobered him more than to at last take stock of the damage he did in his drunken stupor, one he already did not remember save for flashes of tearing and maiming and cursing. It made him realize how he truly did not have as much control of himself as he thought when he drank. He was abhorred by what he saw and recalled, and he spent a few days re-grounding himself. Fixing what he broke however he could without his magic. Reminding himself of Silvanus's teachings, and how important they were to him at his very core. He prayed and meditated and took stock of what was important, about how he needed to continue working on lifting the curse and to be patient with himself, with his god, with the process. He needed to accept what he could not change and act with diligence and patience with what he could, even if he had to do it alone.
Halsin spent probably a few days to maybe even a week out on his own both working to regain access to his powers/regaining Silvanus's favor and in continuing to try and better understand the Shadow Curse. After that time, his connection to nature returned, and he deeply understood the warning Silvanus impressed upon him. It was then that he decided to stop drinking (or to only do it on very very very very special occasions). He did not like who he became that night, and he never wanted to find himself in that situation again. The damage he did was bad enough, but he would never be able to live with himself if he lost control like that again and wrought more destruction than that time or even hurt someone (unfortunately, he probably did hurt some animals, but he did use his traditional healing know how to bring them back to health). It was a very dark moment in his life, and though he did fear facing his demons without the numbing effect of alcohol, he did not want to spiral like that again.
Also little bonus: I like the idea of Nettie helping him kick drinking and keep his sights set on what matters. It would help explain why they seemed to have a slightly better relationship than he did with the other druids and why she has so much faith in him. She knows about his darkest moment and watched him fight through it and ultimately grown from it. But Halsin also respects her not just as his apprentice but as the person who had that care and patience with him during that point. He still kept her at arm's length as he did most everyone else, but he at least allowed it to bend for her.]