How much independency does a postdoctoral researcher have? I am a postdoctoral with governmental grant, means that it is not a grant from a research supervisor for a specific research project. Of course, when I was applying for this grant I was asked to connect with one of the professor in university X and I provided a research proposal. During working on the research related to my proposal, I am working on some other aspects which are not far from my proposed research in cooperation with some other scholars and professors outside of my university. I would like to ask your opinion on whether it is normal for postdoctoral researchers to have collaborations with other people as well?
I would like to ask your opinion on whether it is normal for postdoctoral researchers to have collaborations with other people as well?

Our opinions don’t matter. The professor in charge of your grant is considered your supervisor, and whether it’s okay for you to spend significant time on outside collaborations depends on, and only on, the professor’s opinion. It’s likely okay, and yes it is somewhat normal at least in some disciplines (e.g. math), but you should simply ask them.