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 the vessel’s status as a separate magical item seems to be a bit unclear.
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.