Are the Book of Shadow or Genie's Vessel granted by Warlock features considered as magic items?

Question

Basically the title.

If a Warlock fights by wielding their Book of Shadow or Genie Vessel in one hand as a spell focus and keeps the other one empty to meet the requirement of somatic component, they will eventually end up in situations where they are forced to use the book or vessel as an improvised weapon (like when an enemy closed the distance or when the Warlock needs to perform an Opportunity Attack). So the question is, would hitting someone with the spine of the book of shadow or their oil lamp of a Genie Vessel be considered using an improvised weapon with magical properties?

For the Vessel, It is a tiny object, but not specifically written as "a magical tiny object" even if the previous sentence mention that the patron has imbued magical powers with it. The Warlock can do lots of wacky stuff with it like sleeping in it or dragging others into it to rest, but it almost seems like its the power of the Class Feature using the item in question as the medium in which the feature's power (and thus your Patron's power) is expressed, and not the power of the Item proper.

Genie's Vessel ; 1st-level Genie feature ; Your patron gifts you a magical vessel that grants you a measure of the genie's power. The vessel is a Tiny object, and you can use it as a spellcasting focus for your warlock spells. You decide what the object is, or you can determine what it is randomly by rolling on the Genie's Vessel table.

The book of shadow is even more vague; it is only stated to be a grimoire, and nothing else about it's materalistic properties are mentioned or explained further other than that if its lost or destroyed you can resummon it. How durable is it, anyway?

This also opens some icky boxes like "Would anti-magic fields suppress their magical properties or destroy them outright?" and something like "If the Genie's Vessel is indeed a magic item and using it as an improvised weapon can pierce resistance, the Genie Warlock has access to a magical weapon that is basically the equivalent of a +0 but magical dagger at LV1" etc.

I am aware that some similar questions have been asked, like "Does attacking with an improvised weapon using a magic item count as a magical attack?" and "Are punches with Gauntlets of Ogre Strength magical, improvised weapon attacks?"; but the main issue here is that both the book of shadow and the vessel's status as a separate magical item seems to be a bit unclear. They look very much like tag-alongs to complete a feature's ... uh... feautre.

PS: Before someone says that using it as an improvised weapon is a poor choice of tactics, keep in mind that Genie Warlocks gain extra damage from the "Genie's Wrath" Feature equal to their proficiency bonus. Compared to wielding a regular dagger with the damage of 1d4 + dex + pb, using the Genie's Vessel as an improvised weapon of 1d4 + str + pb isn't that bad; and depending on how the DM would rule it could be counted as magical and be able to pierce resistances.

Answer 1

Neither is a magic item

Note: I do not have access to the Dungeon Master's Guide at the moment, so there may be more detailed rules there, but the Basic Rules have a section on magic items that I will work with.

However, the entire chapter on magic items does not provide any way to determine that some object is a "magic item", and thus I am forced to conclude that the answer to "What is a magic item?" is "Things listed as a magic item." The Book of Shadows is described in the Player's Handbook, but the description does not call it a "magic item" and there is no list of magic items there for it to be on. Genie's Vessel is described in Tasha's Cauldron of Everything, and again it is not described as a magic item, nor is it listed in the Magic Items section. Thus I conclude that neither the Book of Shadows nor the Genie's Vessel is a magic item for anything that specifically says "magic item". That said, you or your DM could rule differently, and there does remain a bit more to the story.

The Book is probably not magical at all

WotC released an official method for determining whether a thing is magical, detailed in this answer, or you can go straight to the source. Of the 5 questions listed, the only relevant ones are "Is it a magic item?" which is no unless your DM is feeling particularly arbitrary, and "does it let you create the effects of a spell that’s mentioned in its description?" which is at least arguable. The Pact of the Tome feature includes these sentences:

When you gain this feature, choose three cantrips from any class’s spell list (the three needn’t be from the same list). While the book is on your person, you can cast those cantrips at will.

There is a perspective that would say "you can cast those cantrips" is at least very similar to "it lets you create the effects of a spell that's mentioned in its description", but I think that "lets you cast a spell" is different from "lets you create the effects of a spell" and this doesn't apply.

Thus The Book of Shadow is a very fancy book, but its special functions are powered by "the background magic that is part of the D&D multiverse’s physics", which by official ruling is separate from things that count as magical for all other purposes.

The Genie's Vessel is magical, and probably makes magical attacks

The Genie's Vessel is more straightforward in being magical. Its description states that it is "a magical vessel" and the official guidance asks "Does its description say it’s magical?" and if so it is magical. This is basically as unambiguous as it gets.

So the Genie's Vessel is definitely magical for things like detect magic that care about that, and since it is both magical and an item there is at least a rationale for calling it a magic item even if I don't agree. Now what about using it as an improvised weapon?

That is also partially covered by a prior question, specifically this answer. The accepted answer (currently) is not the highest voted answer, but it relies on an official errata that came out after the other answer and I find the argument posed quite convincing. It's worth noting that I am judging this for resistance/immunity to "damage from nonmagical attacks" specifically and resistances worded differently may interact in different ways. With regards to "nonmagical attacks", that is almost always interpreted as "attacks that are not magical attacks" and the errata I mentioned defines magical attacks (emphasis mine):

a magical attack is an attack delivered by a spell, a magic item, or another magical source

Thus, even if the Genie's Vessel isn't a magic item, it is still a "magical source" and attacks with it are magical attacks even though it is an improvised weapon while doing so. This is a little contentious (as I said, the relevant question here has a contradicting opinion with many more votes) but has ample support to at least be a valid interpretation.