I strongly dislike your version. Creating a boolean just to use and discard in the next line? Twice? Ugly. I'd much rather keep the code simple and try to cut out confusing parts. Give the flag a better name and remove the useless ternary. I'd also get rid of the conditional return and let the one outside the catch do the work.

  if (!errorLogged || (Math.random() < 0.1)) {
    
    errorLogged = true;
    
    // log error
    
  }

But if it's a choice between comments and adding temporary variables that don't do anything, I'll almost always choose comments.