Mandatory Reconsideration for ESA decision (on Universal Credit)

Here we go again, a few years ago when I was under 16 I had my application for DLA denied, appealed, denied again, went to a tribunal and won with all 3 judges.

Now I'm an adult and I've applied for Universal Credit, and getting fit notes off my doctor as I'm unfit for work due to GAD.
Today I got my result from my work capability assessment, which was on the 9th of February. I am not fit for work. But I am not in the support group, to my surprise. I wish to appeal this decision.
What is the best way to go about this? I have heard online I should call up, request a mandatory reconsideration and tell them why, and also request they send me my report in the post. Is this correct?

I recieve Personal Independence Payment payments at daily component middle rate if that makes any difference.

Also, anyone who has been the same situation? Did an appeal work well for you (I know every case is unique)

Thank you all. This situation is very stressful for me.