Joel Edgerton is truly excellent in his role bringing a very vivid persona to the screen that acts as quite a contrast to the timid Gawain.
The truth is it is an important role because Edgerton's lord is also The Green Knight. At his manor he strikes a deal with Gawain that he turns over to him all he gains on his hunts and Gawain is to give him all he gains while at his manor. What he gains outside of a hand job is the green belt which Edgerton's lord asks him to hand over but Gawain does not want to give up mommy's shameful green belt. So, when Gawain openly fails that test, the kiss on the mouth he gets is basically a kiss of death. Gawain again proves he is no knight.
A lot of good stuff in your post, but, as to the first SPOILER:
Yes, most versions of the classic tale posit the Lord to really be The Green Knight. But, here, Lowery keeps that very vague. He also adds that extended montage where Gawain imagines his future if he hadn't been beheaded. I interpreted it slightly differently, with Gawain finally becoming worthy when he allows himself to be decapitated. And, the Green Knight's true identity is still a mystery.