That’s a great question. I’d need to look it up to give a more precise answer, which might or might not end up being an “ELI5” answer. But it seems like a semicolon works better in that spot because there is more of a pivot than a continuation.

I can see how we might view the second clause as a continuation: it does give more information. His inability to find the book is the reason why he spent so long in the library.

But it really seems like more of a contrasting situation. If he spent that long in the library, we would expect him to find the book that he wanted; however, he didn’t.

It seems like a semicolon works well in your example because we can so easily slide the word “however” into that sentence: “Sandip spent three hours in the library; however, he couldn’t find the book he wanted.”

If you think that a colon conveys the meaning that you’re aiming for, the word “because” probably conveys that even more clearly: “Sandip spent three hours in the library because he couldn’t find the book he wanted.”