Be honest in addressing who and what your apology is even for. Quite often it's a "I'm protecting my bottom line and reputation" and not " I screwed up and need to do better."
Second is to abandon the myth of linear progress which is designed to protect people's comfort to be anti-Black (among other things). There isn't a statute of limitation on racism and it wasn't simply some different time, or you not knowing better because the harm was still caused.
This also goes for other people seeing anti-Black racism from others. No, someone being older doesn't make them exempt from being anti-Black. If someone is too young, then y'all go on about how they're a kid and don't know any better (even when the person in question is literally an adult and you infantilize them.) If they're older, then no, they're not from another time.
There were people who knew and did better at every point in time and we all didn't just recently discover that anti-Black racism was bad whenever you personally learned about it.
Actually apologize to Black people specifically and don't hide on the fence when non-Black people inevitably start harassing whoever the apology was for in the first place. Every single time a situation that necessitates an apology happens there are inevitably people who will run defense for you.
When people are anti-Black, especially in digital spaces specifically, regardless of the anti-Black person's intentions, they represent an almost mythological, thrilling source of joy for non-Black subjects that desire racial violence.
I think that the digital online machine hijacks the mind and body of the disabled subject and uploads them as a granter of that desire regardless of the intentions of the individual person.
They won't care about you personally but will kick up controversy and harass others to protect what they feel is a right to be anti-Black.
If you're going to apologize you have to specifically address this issue too.
Not to "PoC" not "Brown people" but Black people. If it's Black people you're talking about then say that. Digital spaces are designed to produce and grant the desires of those that wish to engage in anti-Blackness. If you're serious and apologetic you'll push back against said people.
Finally if you're going to apologize then actually do it without framing the person you're apologizing to as too much or over the top. When you're Black, especially for Black MaGes, non-Black people always seem to look for any opportunity they can to feel like they can put you in your place or shift blame onto you.
I can give an example where I casually said that medical and research institutions are racist, which they are. Keep in mind I also work in this field myself, so I'm speaking not just from a patient perspective but from a professional one too.
Shortly after I got a snide reply speaking as if I am opposed to the very concept of research when. When I called them out on it and asked them to not speak to me that way, they also just continually replied and demanded I apologize to them despite instigating the situation in the first place.
Personally I'm not really in the business of accepting most apologies from people because I never trusted them to be any good in the first place. But if you're apologizing to other Black people, there are some things to keep in mind.