Apologizing first isn’t losing. It’s deciding the friendship outranks the scoreboard.

Going first in an apology looks like conceding the argument and is actually a separate decision. You are not saying you were wrong about the facts, you are saying the silence has gone on long enough and you want the person back more than you want the point. Whoever moves first usually cares more, which is not the same as being weaker.

If something has been sitting unresolved for more than a few days, send the short version: that you miss them and you do not want this to be the thing. No conditions attached. They may not answer at once, and you will have stopped carrying it either way.