So I had a meta sitting in my drafts before this showed up in the tags under my Claudia post. I wasn't sure how to broach the topic with the fandom being what it is at the moment because this is an extremely controversial subject, but I've seen the same question a couple of times, so I figured I might as well go for it.
It's complicated, because racism, Louis' core wound and trigger, is very much a legacy of slavery that's why he tells Lestat that story about the runaway slaves whose heads were put on pikes in IWTV season 1, which the Armand torture scene mirrors in TVL. I read that for Louis' character, the writers drew a lot from Anne Rice's the Feast of All Saints which is all about the Free People of Color, mixed race people who owned slaves and entered into civil unions (called plaçage) with white men in order to social climb. Which afforded them and their children more privilege but came with it's own unique types of oppression. I tell everyone I see to watch the movie adaptation because it was amazing, but trigger warning for heavy themes obviously. All of this is historically accurate and elements of it are very much present in Louis' story and family background.
Louis is in a unique position of being more privileged than most black people during that time on account of being wealthy and mixed, but still having to endure unimaginable racism on a daily basis. He's uniquely in between power and powerlessness. That complexity about Louis' as someone stuck between privilege and oppression is something I find fascinating about the character and I think it translates well to the other vampires as well. They're privileged by their vampiric power and oppressed by their abusers. This is a huge theme in the story.
Here's the thing though. So far, the only character we know of that has been sold into slavery, lived as a slave, and been actively pimped out as a slave, is Armand. Louis has never been a slave. He's been a victim of racial prejudice, violence, oppression, all the legacies of slavery, but he's never been a slave. The label of slave is something Louis internalized without having ever been through it himself. And yes, the term "slave" is associated with blackness to this day but (1) Slavery is a legacy that most POC have had to deal with in their histories, it's not exclusive to Africa and African Americans - India has it's own history of slavery, some of which Armand personally experienced (2) Most slave masters were white, but not all of them, and that legacy of POC enslaving POC and black people enslaving black people is something that rarely gets discussed because too many people see it as justification to erase the culpability of Europeans and white people and not what it was, a desperate scramble for limited power - power that was limited thanks to said Europeans and white people and (3) The fact that Armand personally experienced slavery but Louis experienced slavery as a historical legacy affords Louis a degree of distance and separation. It's the difference between direct and systemic violence. It's the difference between being called a slave as a slur versus actively having your autonomy taken from you because you ARE a slave. Louis' relationship to racism was very much direct, but his relationship to enslavement wasn't. In fact, the show is consistent about the fact that in many cases, it's the other way around. Louis is the one that enthralls other characters and brings them to their knees.
Louis has consistently been framed as a type of slave master (like he is in the book). His family wealth comes from sugar plantations and Louis continues that legacy when he switches over to pimping to keep his family in the luxury to which they have become accustomed. This luxury is a desperate clinging to limited power. The show frames prostitution and the sex trade as just another form of slavery, which is emphasized when we get to Armand's backstory. He's not just "sold", he's "donated." He can't remember what his parent's named him and he's quite comfortable and happy handing his autonomy over to whoever "owns" him in the moment. Marius, the Children of Darkness, Lestat, and yes, Louis. These are the sorts of things Louis absolutely cannot relate to as a wealthy breadwinner who has always had his freedom (in the direct sense of the word, even if it wasn't always present systemically).
When Armand enters into the relationship with Louis, Louis is the one that holds the power of deciding if or when they're companions. The master/slave or pimp/prostitute dynamic in their relationship is constantly alluded to. Louis calls Louis by the name Armand thinks he had when he's enslaved and their D/s relationship is hinted at. Armand roleplays as one of Louis' servants and talks about how it is a pleasure to serve him. Everything about them points to Louis as the slave owner and Armand as the slave. From Armand's perspective at least.
From Louis' perspective, he's moved on. Jim Crow is over and he atoned for his pimping by giving his prostitutes business shares. Whatever is between him and Armand is something separate and he seems mostly blind to the ways that old pimp/slave master legacy crept into their relationship until Armand makes him think about it in the most unhinged way possible. By reenacting that "runaway slaves with their heads on pikes" story he shared with Lestat that would have made it's way into Daniel's book.
As they revealed in this scene, Armand's background as a slave was barely discussed or acknowledged when they were together. Because, as stated before, it's something Louis can't relate to aside from in an abstract sense. Historical anecdotes about long dead slaves. And we see him acknowledge that he didn't even try. Armand tells him that he lived it and his reaction is dismissal and having the white guy he dreamed up (who also happens to be one of Armand's ex-"owners") scoff. He tells Arun that he's real good at handling things and lets all those little master/slave and pimp/prostitute dynamics slip into their relationship without a second thought about how that might make Armand feel. He talks about Armand's old master grooming him into a little bitch and then self-harms, making Armand question whether he'll be on suicide watch for the next thousand years.
Obviously, the dynamic between them was a hell of a lot more complicated. They were both awful and abusive to each other. They have both abused and victimized each other at different times. They're both in between privilege and oppression. They're both in between power and powerlessness.
Here's the kicker though. They could have found common ground. The label of slave is something Louis internalized without having been through it himself. Which means he has empathy for the plight of the slave. He can see himself in the slave's shoes and understand the slave's pain. But why give that to the person who didn't stop Claudia's death? Why give that to the person he's with to prove a point to Lestat? I mean, obviously that's not the only reason he was with Armand. He was pretty infatuated with him but I think in his mind, Armand was the option that was "safer" than Lestat.
And Armand takes it because leaving Louis is unfathomable. A slave doesn't leave their master. They serve their master until that master dies, sets him free or sells him off. Louis sees Armand's history as another abstract anecdote about a long dead slave, meanwhile that slave is still alive and well inside Armand. There's a huge mismatch between how they view themselves, each other and their relationship.
And fair enough. Armand, like Louis, is extremely powerful and extremely good at acting like he isn't. So much so that Louis never sees him as the actual master of his coven that has power over all these very white vampires or the one who is pretty good at running things himself. Which is why the trial/lynching and Armand's lie about saving Louis sneak up on him. Claudia warns him about Armand but he just can't see it. He doesn't necessarily see Armand as a slave, but he doesn't see him as an equal either. And I'm pretty sure Armand internalized that if his freak out was anything to go by.
For me, the "branding" was about the resolution of all those years of baggage and Armand finally seeing himself as Louis' equal. He carves an "A" into his chest where his heart is (reminder that slaves have no last name) alluding to that scene on the bench where Lestat told Louis that he had his initials inscribed on his suit pocket over his heart (which Lestat says he never did, which means there's something symbolic about Louis saying so). This is when Louis decides to "let Lestat go" and start a companionship with Armand, but he does so by taking ownership of him and calling him Arun. Louis' acknowledgement of the ways he failed Armand and finally coming to grips with the concrete reality of Armand's slavery and how that was a part of how he loved Louis was important. That was Louis setting him free. Not dying or selling him off. Freeing him. The "brand" was Armand taking back his ownership. Assad said that to Armand, it was a romantic gesture. The signature on the contract that set him free. It's acknowledgement that Louis actually did love him.
So, in my opinion, the meaning got muddied because people just saw a generic black character and generic slave imagery, reduced complex historical themes into modern racist stereotypes and just decided to run with it. Not to dismiss the concerns of anyone who had a problem with the scene or a different interpretation. It was intense and dealt with a lot of offensive themes so a lot of the outrage is valid. But yeah. These were some of my thoughts on it.
As for the cast, I'm glad they're leaving it up to audience interpretation. It's tempting to want to tell people what to think when it comes to tricky themes like this, but they're still letting us have fun and engage with it, even if a lot of that engagement is negative. I love the freedom and complexity.