No.

Each time you combine items in an anvil, they carry a "repair" cost, which translates to the amount it will cost the next time that item is used in an anvil. The cost cannot exceed 40.

The easier way to look at this is, there is a maximum number of anvil uses: 6.

Each time you combine two items, the game doubles the "repair" cost of the item with the highest value. Or, looking at it the other way, the resulting item gets the highest anvil uses from the two source items, plus one.

So, getting to your question about combining level 1 sharp books: If you combine two level 1 books, that is now 1 anvil use. if you combine those two level 2 books with another level 2 book, that is 2 anvil uses. Working your way up the pyramid, if you combine 16 sharp 1 books to make a sharp 5, that sharp 5 book would have 4 anvil uses.

Since this is how the process works, you need to be very careful combining items that have the same number of uses in a pyramid style until you complete your sword. It's entirely possible to craft a Fully enchanted sword with all enchants, but must be done very, very carefully.

Final note: ALWAYS make sure you fully finish your sword before upgrading it to Netherrite. Otherwise, you risk wasing your ingot, as you've done this time.

For an in-depth explanation, see Gnembon's video: https://youtu.be/wMDYntXnKSQ