but the argument here is whether nft gives you any rights to his songs, or its just a mere digital signature

That depends on the terms of it. From the looks of it, its just a digital signature. Like a collector's item.

However it can also be used to buy/sell rights to digital works. Just like your signature can be used to sign credit card, loan or just simply sign on your friend's I.O.U. note.

1 btc = 1 btc but is 1 nft = 1 nft? Nft value is tied to crypto, and btc is fungible, nft is not fungible lol

You are comparing Apple to orange lol

You can buy bitcoin or gold and frame it and enjoy it but we are talking about the ownership of NFT and its relation to real world, whether you can actually own the real world rights to it.  As to say when someone plays the name wee song for commercial purpose, can you claim royalty for that?

So what type of right do NFTs give you?? I can take the same amount of money, go to an artist, and buy the publishing right of his song so the song belongs to me, but can NFT do that?