I would suggest that this doesn't need to be an either/or.....but rather an "and". Having a secure run comes in handy in many situations and, generally, those situations arise with such suddenness that building one at the time is not really practical - situations like needing to confine the birds while addressing a predator that has shown up and started dining on the flock. Free ranging is fabulous, but there are times when doing so just isn't the best idea - so having a larger run where the birds can comfortably be housed for days/weeks without leading to issues associated with overcrowding is never a bad idea. Expand the run *and* free range them as much as is practical.
Your coop looks very small to have that many birds in it. I'd almost be tempted to enclose the whole run area into a coop and build a much larger run. Even then, though, I don't know if it would be large enough for 20 chickens. How big are your coop and current run area (in feet by feet)? Recommended space for chickens is roughly 4 sq. feet per bird in the coop and 10 sq. feet per bird in the run. Roughly. In my opinion, the more space the better. Crowded conditions can cause all kinds of behavioral problems such as feather picking and cannibalism.
All new to this chicken thing but be honest with you that Coupe is sold rated for 18 chickens and there's no way for me to guess if that is true or not. Either way they will not be getting a new one or Coupe until roughly about 6 months from now because there is absolutely no way that I can afford to land another $700 down
Unless anybody has any suggestions for a cheaper way to build onto it but that thing was $400 so I'm not letting it go to complete waste and I'm not separating the chickens from each other. Counting again I actually only have 18 chickens I forgot that we lost two baby chicks when they were smaller due to Natural reasons /a type of muscular disease in chickens.
I got about $400 in this coop and 40x80 run. That includes building nest boxes and feeders. You dont need anything fancy for a chicken. A lean to with a couple milk crates will do the job