@Yuai, your H is absolutely flirting with this OW and is letting her know how important she is to him.
This is atypical behavior for him. It sounds like he’s infatuated and is too emotionally invested in her. She is in his head and that leaks out via mentionitis. They’ve built a high level of contact, closeness and reliance. He is always concerned for her, so their KISA/Damsel dynamic provides mutual validation, as does her knack for cheering him up. Chatting with her energizes him.
I suggest your reading Not Just Friends by Dr. Shirley Glass. She explains how marriages/relationships are threatened and damaged when one partner opens a window to a third party and blurs boundaries by channeling more and more emotional resources into her/him. Many emotional and physical affairs begin this way.
In your H’s case, their frequent contact, confiding, laughter, in-jokes, commonalities, etc. are deepening their intimacy and strengthening their connection. Meanwhile, he is creating distance between you with his moodiness.
You made my day and I know you feel the same.
@Yuai, I wouldn’t tolerate this. He’s playing with fire and it’s happening right in front of you. In my view, this is already an emotional affair. A very serious conversation is in order, and he needs to read Not Just Friends.
If he’s in too deep, he may push back to protect their relationship using manipulations such as dismissing your discomfort, defensiveness, denial, minimizing, or blame shifting. Don’t allow any of that. Tell him that he has everything to lose if he doesn’t tighten his boundaries and distance himself from OW. If he cherishes your marriage and values your well-being and peace of mind, he will do that.