While I've wondered the same exact thing, I think there's solid reasoning for him not to wear it.
The purpose of the new look is "symbolic". It's meant to show that he's trying to step out into the light, as well as trying to overcome the darkness within (which was the reason why he wore the black suit in the first place after Jimmy's death, because inside he was dead to his human instincts until Lois came back.) He kept wearing the black suit because he didn't see a problem with it.
But after Cat mentioned the world needed a hero in Red and Blue, as well as Chloe saying she saw him, along with the fact that Clark knew he needed to step out into the light and stop hiding, all of that led to the decision to wear the new look.
Now, he didn't wear it in Supergirl because he didn't really go out for a save. He saved Lois, but first he had to go look for her in a public crowded place. So he didn't really have a chance to change or even a need to for that.
In Homecoming, there was no need for it either since he didn't go out to make a save, except for in the future, but he didn't have the jacket with him there.
In Isis, while it would've seemed likely that he would've wore it at some point there, he really didn't go out to make a save. He was looking for Lois, so I could understand why he would wear it, unless he wanted that to be the way he revealed his secret, though i think it was obvious that he was going to continue hiding it a little longer until Lois convinced him that she was ready.
Personally, I can't wait to see him wear it in action, and I'd also love to see Lois' reaction, as well as the public to see if they will go back to the RBB or come up with a new name. But there's still 17 episodes left and I'm sure we'll see him wear it at some point.