Why did my ex-boyfriend ask me not to bother him and his girlfriend, and I won't bother him? Why did he comment on me and send me an anonymous message "In fact, you are very important"?

Personally, I suggest not to disturb your predecessor too much and have a sense of boundary. Now that we have broken up, let's move on, live a good life and find a new relationship.

Regardless of whether the message "Actually, you are very important" was sent anonymously by your predecessor, ignore it. If you don't come from your ex, then if you bother him again, it will appear that you can't let go of this relationship and the other party has a new girlfriend, so you should adapt to this reality and adjust yourself as soon as possible.

If the news is really sent anonymously by his predecessor, then personally, you don't have to pay attention to him. He already has a girlfriend, and sending you such an ambiguous message shows that he is half-hearted and insincere about you and his current girlfriend.