I got banned on the server for accidentally logging on with lunar. Am I allowed to use a different account to continue playing or is it an IP ban?

In Game Name: LeoClover

Reason for my ban: I was banned for accidentally logging onto the server with lunar client because I had just previously been using it on my own survival world. I then told a player that I would be right back as I didn't mean to get onto lunar client and then proceeded to leave the game to switch to regular java edition which is of course when a storm came and wiped out the internet. I then logged on an hour later and about 5 minutes after logging in, I got banned.

Why should I be unbanned: It was just a little human error because I just forgot that I was using Lunar, even though I just left almost immediately. I also never used any mods like waypoints or any other things that would give me an unfair advantage to other players. I apologize for this and I will make sure to double check and switch back to the regular Minecraft launcher if it were to happen again.