I was going to ask for information on the specific coop. Thanks.
If that were mine I’d take off the end opposite from the coop section and build the run extension there, or since you have to assemble it, just leave that end off. There are so many different ways you could do it it’s hard to settle on one. If it were me I’d probably set four fence posts in the ground to make it really stable and wire it in, remembering to make a door. Set that coop/run so the side you tore out can be framed into one of those run frames. Since most building material come in 4’ or 8’ lengths I’d make the new run extension 8’ x 8’.
That coop/run is only 29” wide. I’d worry about it being stable in a high wind unless you anchor it.
There will almost certainly be times that you will wish to leave them locked in the run and coop instead of out free ranging. In my opinion most of the behavioral problems people have with chickens is because space is tight. Be generous with run space. You are wise to think about that ahead of time.
If you can provide reliable electricity to that coop there should be no need to keep them in the house at all. Many of us brood outside straight from the incubator or post office. You need to keep one area reliably warm and let the rest cool off some so they can find their own comfort zone.
On challenge to brooding outside is that your daily highs and lows can vary a lot so it is really difficult to keep the brooder/coop a constant temperature. You don’t have to. Just keep one area warm enough in the cold and another area cool enough in the heat and they’ll take core of management details.
I use heat lamps, others use ceramic heaters. I’ll give you a link to a popular method that makes a cave out of a heating pad.
Mama heating pad