How can I appeal a mistaken suspension?

That is very true, just wish the game chat work though lol, thanks for explaining and have great day

Well if you read the screen when you are posting thr lfg it clearly states LOOKING FOR GROUp only

https://support.xbox.com/en-CA/help/friends-social-activity/friends-groups/using-looking-for-group

Think of Looking for Group as a “players wanted” bulletin board—a way to help you find players in the Xbox community with similar goals and interests. Browse posts created by the Xbox community and respond to those that appeal to you. Or, try creating your own post—when enough people are interested, gather them into your party and go play.

Plus, it's easy to take your Looking for Group activities with you across your devices—it's as simple as using Looking for Group in Game Bar and continuing where you left off on your Xbox console, or the other way around.

If you check forums there are loads of people who get suspended for the same thing correctly

Mmorpgs have specific channels for things like clans trade etc

You have to do trades in private or party chat or trade channels NOT lfg

You will also get suspended by devs if you break chat rules governing channels this isn't new

From the code of conduct

https://www.xbox.com/en-CA/legal/community-standards

• Sell in-game content outside of official in-game mechanisms and stores
  
• Trade game lessons for Xbox gift cards or other compensation
  

LFG is NOT ingame

Games tend to have their own lfg or matchmaking channels though but usually they will have their own trade channels

Have you gone into game chat via an xbox party or via fall out it's self?

If you were banned by bathesda then microsoft won't be able to over turn that decision you could try to contact bathesda and see if they will over turn it however this is unlikely as someone said earlier the Devs have their own rules.

https://www.xbox.com/en-IE/legal/community-standards Basically comes under fraud benefits no one. I know you're not selling, but you are trying to buy from someone that is. The best place to do it is social media.