I think forgiveness is important. There are certain people and things in this hobby that I've forgiven, both because there have been apologies and definitely there's been no apologies. The first is nice- sometimes really nice, if for no other reason that you feel seen and heard about how something was hurtful when it didn't need to be. The second is more of a function of needing to just move on in life. Here again, I'm not waiting around for someone to pony up on apology but you run the risk of getting stuck in a sentiment or a feeling that doesn't do anything productive and just makes you feel like shit.
I also think sometimes you do things that are upsetting to someone else and apologizing isn't enough or for whatever reason, trying to offer one is the wrong idea. I think in those cases, if it's not enough or you just think attempting to apologize is going to be more harmful than helpful - you just have to agree to learn something from it and not repeat that behavior.
I've been in this hobby a long ass time. I started mushing in my late teens as a way to escape an abusive situation at home. I had a lot of coping and survival mechanisms from my real life that I imported into mushing because I'd gotten by in life on those so why not in virtual space. One of those things was trying to overly manage other people's feelings. Children in abusive households often become hyper sensitive to everyone else's emotional barometer and when things are too hot or too cold, they work hard to please the situation. I am/was certainly no exception to that experience, I'm a grown ass adult but I still catch myself doing it.
One of those things that's an extension of all this is passive aggressiveness. For me, it stemmed in being ultra terrified of any sort of confrontation. In my young life, confrontation wasn't about disagreement - it was volcanic displays of fury that sometimes got the cops called. So, the next and only thing to do was to swallow your feelings, avoid confrontation, and pretend everything was just fine. Regardless of being aware of where it comes from, it didn't serve me well for a long time in the MU* wider world. I certainly ruined some otherwise positive and happy online 'working' relationships and friendships because I was ultimately too terrified to just say something that might be upsetting.
I've been through a shitload of therapy as an adult because I got tired of feeling like garbage about this. I have much more clarity and self-awareness around this behavior but because I'm a flawed human being, I still feel myself slipping back into familiar territory. I'm generally much better about it and behavior in general. As much as anything is a work in progress until we no longer draw breath.
But there are cases where I can't find the person in question that I didn't behave well towards because time and the closure of games. In some cases, I've no idea if these people even remember those choice moments - they probably don't and chances are, that momentary blip of conflict was just that for them. But believe me, I remember those blips.
There are cases where I think I know how to find people from the past but I'm not sure they want to hear from me. I don't want to invade boundaries just to offer an apology as that seems like anti-thesis of the point. In both those cases, all I can really do is not repeat my mistakes and missteps, even if that player never knows about it. I guess that's how you prove that you're trying and hopefully succeeding at being sorry for what happened - by trying to avoid repeating the same pattern.