It should be at least legendary.
There is a bunch of official items from Tasha's Cauldron of Everything that work in a similar way of the proposed item: Alchemical Compendium, Astromancy Archive, Atlas of Endless Horizons, Duplicitous Manuscript, Libram of Souls and Flesh.
All of them have 3 charges, and they share a common option:
If you spend 1 minute studying the book, you can expend 1 charge to replace one of your prepared wizard spells with a different spell in the book. The new spell must be of the [X] school.
The sole difference is the school to which the new spell must belong to, which is thematically linked to nature of the item. Each one present another option (that costs 2 charges) linked again to the theme of the item. These items are listed as Rare.
Since they are providing a similar mechanic to the proposed item, one has to compare the aspects that look alike:
- The substitution option can be taken 3 times per day, in ideal conditions (3 charges left).
- The new spell must belongs to a particular school of magic.
- The change takes 1 minute.
- The wizard does not have to leave out one slot from the prepared spell list.
The proposed one instead:
- The substitution can be taken once per long rest.
- The new spell can be any in the spellbook.
- The substitution is instantaneous and does not require an action, a reaction or a bonus action.
- The wizard has to leave one slot from the prepared spells list free.
There are two aspects that seems to set the power of the Uncanny Book at a lower level than the spellbooks from Tasha's, namely 1) and 4), but the other twos allow the wizard to be incredibly versatile, since just with a thought they can choose any spell from the spellbook that may save their life, solve a problematic situation, or whatever hard situation that they may encounter.
There is another magic item that provides a similar option, the Crystalline Chronicle:
- If you spend 1 minute studying the information within the crystal, you can expend 1 charge to replace one of your prepared wizard spells with a different spell in the crystal.
- When you cast a wizard spell, you can expend 1 charge to cast the spell without verbal, somatic, or material components of up to 100 gp value.
The first bullet allows the change of prepared spell, without leaving out a prepared slot and without any limitation on the school. Anyway, it still requires 1 minute for the change. The rarity of this is Very Rare.
Even in the first tiers of play the Uncanny Book could be a game changer. For example, a 4 level wizard has 12 spells in the spellbook (by following the rules in the PHB and without considering additional spells provided during the adventures by the DM). They can prepare a maximum of 8 spells, supposing that they maximized the INT score. Using this item, the wizard can prepare 7 spells, choosing to leave out some that may of some use in particular situations, for example the Shield spell, since they know they always managed to be out of the fight, or the Mind Spike because they are not planning to read thoughts. But by using this item they have the whole spellbook at their disposal in an instant, being hence ready to adapt to a large range of situations.
This further versatility to the Wizard class makes the Uncanny Book's rarity (strictly) greater than the rarity of one of the items from Tasha's: it elevates the rarity of the Uncanny Book to Legendary, not even Very Rare, even comparing it with the Crystalline Chronicle, since the latter requires 1 whole minute for the changing.
Actually, there is another item in the DMG, the Tome of the Stilled Tongue, a legendary item providing (again) a similar option for casters:
If you can attune to this item, you can use it as a spellbook and an arcane focus. In addition, while holding the tome, you can use a bonus action to cast a spell you have written in this tome, without expending a spell slot or using any verbal or somatic components. Once used, this property of the tome can't be used again until the next dawn.
In order to cast any spell in the spellbook, this item requires to use a bonus action but the caster does not spend a spell slot, while the Uncanny Bookmark allows to do this using an Action (the Cast a Spell action) but at the cost of leaving one "preparation slot" free. The provided feature (casting any spell in the book) is the same, but the Uncanny Bookmark has a slightly higher cost (leaving a "preparation slot" free), which is not so impactful, due to the high number of spells one can prepare. Supposing that the DM is not very generous, a 20th level wizard has 24 spells in their spellbook and they may prepare 25 spells, provided they maximized their INT score. The cost is hence negligible.
The real power of both items lies in being able to cast an unprepared spell: but the Tome allows to do this per day, while the Uncanny Bookmark allows to have that spell prepared until the rest of the day, hence the wizard can cast it multiple times, provided that they have slots available.
From a game balancing point of view, we have to remember that the 5th edition of Dungeons and Dragons is highly in favor of the players, and the wizard class is really powerful and very versatile. Using this item augments the power and the versatility of such class, against other classes, and further eases the game, allowing the wizard to access and to use spells in their whole spellbook in an instant.
To be honest, I do not think that I would use this item in my games as a DM: I could give it a try in case I consider this as an artifact designed for wizards that, among other properties, presents this option for delayed spell preparation.
Otherwise, since there is already a magical item that provides a very similar option to what yours item does, I suggest to use the Crystalline Chronicle.