I ended up joining a round I think milliseconds after someone already got a kill, (For Medal, which is my clipping software, I had it so it only clips up to 1 min and 30 secs. I got the full run recorded but not me in the menu/on the loading screen.. sorry.)

Would the run be considered Standard or Late in this case and would the run still count? [Also, the top hasn't had time to get updated yet either when I joined, so my avatar isn't there.]

assuming you deployed just after the round started and set the time to be the same as the end game timer it can be counted as standard. late join is typically used when someone deploys multiple seconds late