I’d focus on how it makes you feel. It doesn’t really matter what he is doing in my opinion. How you feel is more important. Some people would not care if their significant other flirts. Someone on here posted they wouldn’t care if their partner is having sex talks online. Some might be fine with partners sleeping around.

Seriously it doesn’t matter what people do.. In my opinion what matters is how their actions make you feel. He might not be flirting. But what he does bothers you, so that matters.