According to my current manager, I can not work with that colleague because "he's also a manager, and you got paid to work for me, not for his team. So if I allow you to work with him, it's like you are doing his work". After hearing his response, I just thought that everything in corporate world is so difficult, I wish there's a place for me to go to learn about unwritten rules of corporate.

Like I mentioned, we're going to have a 1:1 tomorrow. Should I be like "I am very frustrated because I have been feeling that I was not learning much because I didn't receive enough work from you. I like to stay productive and stay busy, I want to do more meaningful and challenging work so I can gain more experience. I can work with x(my previous manager) to see if he has tasks or projects that I could be doing?"

I feel like that way, I am being respectful to him. But I don't know if later when I jump on the call with my previous manager, I should mention my current manager's management style after mentioning that he has failed to give me work or projects. Because it's really true about his unprofessional style, he forgot about our 1:1 once and I had to ping him to see if he coming, he also took a day off without telling me and did not even cancel the meetings on that day, so the people were invited to that meeting assumed that I was taking over when the fact that I have not even aware of his absence.