At least in some countries authors get a compensation every time their book is borrowed from a library. So you might still be indirectly supporting the author when borrowing from a library. Also if there's enough demand, the library may acquire additional copies and the prices for libraries are higher than for consumers.
Conversely, when you are borrowing a book from an author you like, you probably are supporting them and do not need obliged to purchase it for yourself.
At least in some countries authors get a compensation every time their book is borrowed from a library. So you might still be indirectly supporting the author when borrowing from a library. Also if there's enough demand, the library may acquire additional copies and the prices for libraries are higher than for consumers.
https://equityatlas.org/how-do-authors-make-money-from-libraries/
Conversely, when you are borrowing a book from an author you like, you probably are supporting them and do not need obliged to purchase it for yourself.