Textures: (I have tested each texture and model individually)
[media]Items:
/give @s minecraft:writable_book{CustomModelData:1}
/give @s minecraft:written_book{CustomModelData:1}
Here is a video to better display what is meant. When signing the writable book the CustomModelData NBT data is not transferred to the created written book.
[media]
This issue relates to MC-138892.