"We sincerely apologize for any harm..."
While there are other requirements, a sincere apology cannot in any way entertain doubt about the fact that there WAS harm.
Truly acknowledging the harm done is foundational to a real apology, and most of us (myself included) end up sneaking in weasel words or phrases like this.
Psychologically, its nice for the apologizer, since it allows one to think "i'm being good by apologizing, but maybe I didn't do anything bad after all?".
But from the apologizee standpoint, these phrases are often devastating and can make it clear that the apologizer has no real recognition or care of what happened.
Personally I've worked pretty hard to try to remove these sorts of phrases from my apologies. It's not easy. It makes you feel much more vulnerable and you really have to let whatever you did sit with you in a very uncomfortable way. But it's worth it.