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I would like to know what (なんだけど / なんですが) means? I think these two forms are the same, but when I asked in class their meaning, I was told that they mean nothing, so I'm kinda confused.

For example, in this short sentence: そのことなんだけど, what is the function of (何 + だ + けど [softener])? It appears in: https://www.youtube.com/watch?v=s7xM_NVn5Vc minute 3:32

Besides of its function, are there any grammar patterns or any particular cases in which なんだけど should be used?

Thank you so much in advance for your help and your explanations!