That’s exactly the difference between a colon and a semicolon.

A colon explicitly relates the two statements. In your example, a colon would indicate that he spent three hours in the library because he couldn’t find the book. A semicolon would leave it open to interpretation: he couldn’t find the book, but that’s not necessarily why he spent three hours in the library.

So yes you can use them in the same sentence but not interchangeably. They have different meanings

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.”

Yup. Colons, semicolons, and commas have a lot of overlap. There aren’t rigid divisions between their use and a lot of situations where some or all of them are valid.