I have something similar and I decided I’d rather have a few holes in the furniture than have the whole thing come off the wall or fall on the TV. If, someday, you decide to use the bookcases differently it’s easy to patch the holes with wood putty. Try to find a stud behind each bookcase and screw them to the wall. Add screws to the bridge to make sure it’s firmly attached to the bookcases. I know it hurts to drill holes in new, expensive furniture, but for your safety and the safety of the new TV I would do it. Just try to make the screws as inconspicuous as possible.
I’ve had a grandchild try to climb a bookcase once. Luckily I was there to catch the case before it tipped over. Since then I ALWAYS mount them to the walls. I’ve used little “L” brackets on the top or screws through the back wall into a stud, whatever works the best and is the easiest to hide.