a picture so we can see the FP would help

I’m so Envious 13 foot ceilings. We only have 9 1/2 foot ceilings but when my husband built these bookcases he went clear to the ceiling and then added crown molding.

IMO bookcases need to be designed to function for what you want to put in them. I certainly can’t see bookcases to the ceiling in a 13’ wall unless you have 1000s of books.I acyually find most people put bookcases in to add a whole bunch of stuff that does not need to be displayed I find a cabinet on either side of a fireplace with the TV mounted above one and a piece of art above the other a much less cluttered look but that is me. Think about what you want to display and build the bookshelves to accomodate it just like you don’t use the ceiling height to hang art you don’t use it for this application

How much linear space do you need for shelving?
Maybe think about that first.
You don’t have to have all shelves.
You can have enclosed storage on the bottom with doors, (maybe double doors) on each side that go up 3-4 feet.
You can use the enclosed storage for things like games, chess, backgammon, audio- visual equipment, and logs and matches for the fireplace if it is wood-burning.
Also a good idea to keep there are things for entertaining in that room such as coasters, cocktail napkins, candles, a tray.
You might want to think about whether you want simple shelves behind those doors or deep drawers which obviate the need for kneeling down and sticking your head in the back to look for something. Another option is a shelf that rolls out on a glider mechanism. And you can add a “lip” of a few inches at the front so small things don’t fly off. You can also have one drawer at the top for the smaller things like the coasters, candles, matches, candle snuffer, etc.
Once you have that you do that on each side you can do shelving the rest of the way to the ceiling.
I would request shelving that is adjustable, and that is very thick, so it doesn’t bow with the weight of books.
Do remember to add attractive molding on the sides, top and bottom of the shelves as that is what distinguishes custom, finish carpenter work from simple IKEA shelving.
Of course you will know how to arrange things on your shelves so they look attractive.
You can have books, live plants and interesting objects that you collect or fancy that are large enough to be clearly seen from the seating area. Works of art can be displayed by hanging them from the edge of the shelf.
There might be a place in the room or a nearby room for you to store a step- stool to get things down from the uppermost shelves, but if the things at the top are not what you would really need, you will be fine.

Thank you so much for all the information and ideas that I need to consider.