You don't really need to read something as specific as anarchist theory to challenge a bias towards Leninism.

If Leninism itself leaves comparatively too much to be desired, or plenty of other strategies have something sufficiently desirable that Leninism lacks, that's enough to challenge Leninism.

Anarchism is a very specific strategy, centered on prefiguration, as well as effective and horizontal power building that developed in Europe in response to an increasingly industrial society. But of course, plenty of effective and horizontal power building movements arose in response to different conditions and weren't anarchist. The Zapatistas are explicitly anti-anarchist (though another commenter in this thread you were interacting with seems to be implying that they self-identify as anarchists and it's the rest of the world that refuses to acknowledge them as such???), and are an anti-colonial movement centered around a national identity of being colonized.

What distinguishes anarchism is that, because it is in response to industrial society, it developed strategies specific to a structural analysis befitting industrial society. Even if nothing about anarchism turned out to be compelling to you, there would still be plenty of room to challenge Leninism. The organic centralists of the ICP have plenty to say about Leninism, as do councilists, and all of these theories share with anarchism all kinds of desirable things that Leninism lacks.

But that said, a pretty comprehensive reading to get an idea at least for what contemporary organizational dualists are up to these days is Turning the Tide which was published May of last year.

As for why it shifted to anarchism, so for background, it was for a while just sort of sympathetic to both historical materialist-style communist strategies (what you call 'Marxism,' henceforth 'histcom') and anarchist strategies. Namely, a lot of left-communist doctrines and anarchist doctrines had a great deal of predictive and explanatory power, and seemed to provide a plausible way to combat the ubiquity of domination (especially the domination of nonhumans, which was of particular interest to it). So it was never a Leninist histcom, but it was pretty sympathetic to histcom approaches.

Two things make histcom approaches extremely unappealing. First, histcom texts and discussions are extremely unconducive to filling in holes in their structural analysis. Be honest, how much success have you had explaining suicidism to a group of Leninists who've never heard of it? How much success would you expect if you did this: Go from Leninist group to Leninist group. They aren't antecedently anti-psychiatry. Make them listen to mad people about why therapy and psychiatry must be smashed at all costs.

it can tell you from experience that your success rate will be very low. Leftcoms have this problem to a great extent too. This is a problem. At the pro-Hamas actions where it is, a Leninist group that hates queer people keeps trying to infiltrate the actions and capture members, the majority of whom turn out to be queer or queer allies. That is truly how far behind their structural analysis is, putting aside the fact that they're a well-known abusive cult here. This is not cherry-picking, it is par for the course for large Leninist groups with local chapters everywhere to have no cognizance of anti-queer violence, sanism, suicidism, speciesism, no conception of what heteropatriarchal slurs are, no willingness to understand the transmisogyny of punitive degendering, just a total lack of analysis of our objective or subjective conditions.

Second, histcom texts and discussions are extremely incapable of recognizing abuse, or even conceiving of what abuse even is, and it's often downplayed! Abuse is, to be clear, a huge issue in anarchist spaces, especially Food Not Bombs chapters. It's not specific to any tendency. But after starting a pro-survivorship specific organization nearly a decade ago, what it's found is that anarchists have the tools to unlearn abuse and learn what abuse is. To recognize that abuse is ubiquitous, that we are all born fascists and colonists and must unlearn that violence, that to address abuse is to assume it will occur and to study, analyze, and plan accordingly.

Histcoms, and especially Leninists, are not in a similar position. And this seems to be a phenomenon that owes itself to the origin of both traditions. Where anarchists are incredibly willing to recognize Bakunin's treatment of his Jewish comrades and the incredible trauma and pain that must have caused, histcoms are generally extremely unwilling to admit to Marx and Engels's pattern of forming abusive relationships with those more vulnerable than them and forcing them into isolation. Or, they're unwilling to really put themselves in the uncomfortable position of really sitting with Lenin's choice to harbor Bauman after Bauman drove a woman to suicide by abusing her over a long period of time. To really sit and internalize what she must have felt, what she would have felt knowing Lenin upheld Bauman to the point that he is today memorialized with a statue while she is forgotten, having gotten to achieve nothing.

it thinks it understands why Leninists and mainstream Leninist texts so frequently do this. This denial is a way of maintaining social strength. If you admit to atrocities, it makes your ideology less appealing. But it sees it differently. If you are willing to sit with the atrocities and the pain of your ideology, and really grapple with the mistakes in analysis and action that made those atrocities possible, then you're willing to do the work to ensure you don't immediately drive off victim-survivors. Abuse denialism doesn't wave a red flag with a yellow hammer and sickle, it just raises a red flag. One that says "you'll be victimized here too."

Addressing abuse among revolutionaries is such a pressing issue, and over and over histcoms (including some leftcoms!) glorify their favorite figures, deny the historical record when it says these people are abusers, even to victim-survivors. How could anyone reasonably conclude that a tendency that consistently does that over and over could ever be the right path forward?

Abuse among anarchists is just as ubiquitous, but if you talk to an anarchist about power dynamics as being central to abuse, they won't hazily quote Engels's "On Authority" at you and say the concept of 'power' is reductive or whatever. They'll understand. And they'll genuinely improve and do better next time when figuring out who to deplatform and who to empower. They'll recognize anti-survivorship, they'll recognize when some org refuses to center a victim and is kicking out an abuser for appearances without actually listening to what the victim wants or needs for their safety. Anarchism just has a better fucking track record at being a bulwark against chauvinism and abuse.

it was never really sympathetic to Leninism in particular, but it was sympathetic to other histcom tendencies, and to some extent it still is. But a lot of love's been lost from these experiences, and hopefully that answers your question of how it shifted from histcom-leaning to anarchist-committed.

But as it said above, if you don't find anarchism convincing, it would far sooner you gain an interest in the ICP than sticking with Leninism.