[RPG] Do I need to use the Arcane Grimoire as a spellcasting focus to gain its bonuses

dnd-5emagic-itemsspellcasting-focusstacking

The description of the arcane grimoire magic item states (TCE, p. 120; emphasis mine):

While you are holding this leather-bound book, you can use it as a
spellcasting focus for your wizard spells, and you gain a bonus to
spell attack rolls and to the saving throw DCs of your wizard
spells
. The bonus is determined by the book’s rarity.

I do not understand the purpose of the word "and" after the second comma. Hence why I still have this question in my head:

Do I need to use the arcane grimoire as a spellcasting focus to gain its bonuses?

If a wizard does not need to use it as a spellcasting focus to gain its bonuses, they could very well "stack it" with an imbued wood focus (ERLW, p. 277; WGE, p. 114):

An imbued wood focus is a rod, staff, or wand cut from a tree infused
with extraplanar energy. If you're a spellcaster, you can use this as
a spellcasting focus.

When you cast a damage-dealing spell using this item as your spellcasting focus, you gain a +1 bonus to one damage roll of the
spell, provided the damage is of the type associated with the item's
wood.
The types of wood and their associated damage types are listed
in the Imbued Wood Focus table.

Best Answer

You only need attune to and hold the book to gain the bonuses to spell attack rolls and spell save DC.

Arcane Grimoir states:

While you are holding this leather-bound book, you can use it as a spellcasting focus for your wizard spells, and you gain a +1 bonus to spell attack rolls and to the saving throw DCs of your wizard spells.

The only requirements for gaining these benefits is that you are attuned to and holding the book. “You can use it as a focus” indicates that using it as a focus is optional. There is just nothing here to indicate that using it as a focus is required for getting the bonus to spell attack rolls.

Contrast with the Fernian Ash Staff mentioned in the question:

When you cast a damage-dealing spell using this item as your spellcasting focus, you gain a +1 bonus to one fire damage roll of the spell.

This item explicitly tells us that we must use it as a focus to gain the bonus. In the absence of an explicit requirement, we conclude that no such requirement exists for the Arcane Grimoir.

However, if using both of these items at the same time, you could potentially run into issues casting spells with Somatic components but no Material component, as you have no free hands. Taking the War Caster feat, which every wizard should do in a game that allows feats, resolves this issue.