Luminara did not give up on Barriss
I keep seeing people say that Luminara was cold and wrote off Barriss as dead, but I personally do not agree with this take.
When the padawans detonated the droid factory, Luminara and Anakin had no idea where they were, and the padawans were literally about to suffocate had Ahsoka not found a way to send that signal. Luminara was mentally preparing herself for the possibility that she would lose her padawan, who she did care a great deal about. And her instinct about losing the padawans was correct - the padawans were so close to dying.
Keep in mind that as an experienced Jedi master, she could sense her padawan’s life drifting away through the force, and her instincts were right. Barriss was moments away from suffocating. But as soon as they receive that signal, she jumps into action to save her padawan, and you can see the visible relief and happiness on luminara’s face when Barriss is alive.
As the rescue was underway, Luminara was being calm and mentally bracing herself for the very likely possibility. I think that pairing Anakin with Luminara showed his inability to let go, which as we all know, would have massive consequences for the galaxy. You can tell Luminara was very happy to see that her padawan survived the mission. She says that she will celebrate her padawan if Barriss passes, and I think people miss this part. All in all, I think people mistake her calmness and ability to let go with her being cold.