Is it normal to see my own domain (created as a project in Serpstat) to show up in the "Competitors in organic search" report?
It is very common. It seems to be the way that Serpstats works. I just checked half a dozen sites and every single one of them was listed as its own competitor. Here is a screenshot of the report for "stackexchange.com":
I'm not sure how they order that chart. It appears they always put your own site at the top of that list. For example, here is a screenshot of the report for "stackoverflow.com" which was listed as the #4 competitor for Stack Exchange: