Like you said, most apologies are made for white allies and "allies" to make them feel better about supporting them. Due to this, most of these apologies are overly vague, uninformative, and not disarming.
This is a long one because frankly it's been so botched up that it needs to have a lot to it.
All apologies regardless of reason require a) Proper address b) An understanding of the action c) Layout or evidence for change. This is Apology 101.
A) An apology won't be an apology if it doesn't address the offended party. If you just say "I'm sorry to you all" instead of "I'm sorry to Black people" or "The Black Community", etc., then that makes the incident easier to downplay. You're already showing that you're not actually sorry because you're too careless and/or afraid to address who you actually offended. It's as easy as just saying our community or people. It must be the first thing and it must be clear.
B) You need to show that you know what you did and it's severity. Actually fully write out or say out what happened. Not just "we said some really bad things" or the adjacent. Also do not leave out previous incidents. For the most popular recent example, Kovach's first part of part B is fair but it leaves out his "Black History Month" rap for Hellaverse where he further slanted against the n slur MULTIPLE times. That should've been in the apology, not just Jackbox. But notice how I said first part. Now you've explained the incidents, now explain why they are bad. Yes, this apology requires research. That's how serious the offense is. If you didn't want to do the research, don't do the racism. It is that simple. For example of the n slur, explain why the slur is bad. Don't just say "it's offensive to Black people". Explain the dehumanization aspect. Brief on slavery. Show that you actually understand why the word is bad. Apply the same for other offenses like monetizing blackface or racial stereotypes of Black people for humor and/or shock factor. Mockery of blaccent and AAVE. Lying about how Black movements worked and Black culture and/or downplaying the situation when you're not the offended party I am still waiting on that one. Now that you've both thoroughly explained the incident and why it is bad, NOW there's groundwork for change. This also helps disarm white knights as you're showing why what you did was bad and shouldn't be defended. Don't forget to include that you shouldn't be defended at all. Deliberately say that.
C) For incidents from years ago that still matter today btw in the well alive working animal of structural racism, you have to at least show change if you're going to cry "it was x years ago!". So far I haven't seen an offender change. Never. What do they have in common? They either never apologise or make a lackluster apology. If you've followed A and B, then C should be a natural next step. Change. Sometimes donations to Black organizations like BLM can work. Actually if you go to the BLM website you can find other Black networks to donate to. But the BLM websites doesn't have all Black fundraisers ofc. Maybe support a Black person in the same field as you, but do not be surprised if they reject. Make your space and community nicer to Black people. That's actually the most important. Not a influencer/known creator? Call out your friends and family for their antiBlack racism. Try to help out at stuff like food banks esp if you're in a west country, I've did it and most customers were Black so helping poor aid programs spill to Black aid too. No matter where you are, unless by genocide then that's a new problem, there will always be Black people. So there's no excuse. Find any form of aid for Black people in your country. Learn about where Black people are whether economically or location wise and support aid to those demographics. This doesn't just or only have to be monetary, promotion and sharing with those you know helps too. of course another important one is working to be an ally in an never ending fight for rights. Also spread awareness. Any monetary method will fall flat if you don't do A and B as throwing money to the problem is a common escape so when in doubt learn to be an ally. Of course you need to actually change. That also includes reading and learning about Black people. Black media is a thing. Resources too. Even if you help Black people if you are still racist then it doesn't matter. You need to actually change. Drop habits. Drop the humor. Change is a combination of internal and external shift. I've been through it, if you just say you're gonna change and do nothing then you didn't change. If you do something but internally still have the same biases, you didn't change.
Secret Part D) Never ever hinge your apology on acceptance. Your apology should be hinged in fighting racism, but especially racism in you. If you hinge your apology on only acceptance and Black people don't accept it even with the right bells, then you'll just give up and you'll still remain the same level of racism you started with if not worse. Your apology is to battle racism. It's to battle a genuine cause. That also includes no moping. No white savioring. No "I guess critique is what I get for what I did" because the offended party has it much worse than you. How about you say "and still Black people face hate from my fans after my apology. That is not okay and Black people should be supported not hated". No woe is me. This apology isn't about you being accepted alone but primarily on fighting an entire war of racism. Of antiBlackness specifically. If your apology is only made for brownie points, it will never be enough. Understand your role in racism. It's the only way you can improve. If you really need to center yourself, then this apology is to save you from racism.
The apology ofc will be long but it doesn't have to be an entire college essay either because I know some people will complain like that. Like no, you can fit all of this in like one or two paragraphs.