For the question whether VNs are a medium of their own or a genre of games, I have to say: both. It's all terminology.
To examine how that works, let's look at another thing that can be both a medium and a genre: RPGs.
An pure RPG has a number of very specific trappings.
-Focuses on a character/set of characters and their acts and deeds
-Character advancement (levels, ability points, skill training, etc.)
-Provides a narrative, with goals and rewards (quests)
-Gives the audience agency when forming the narrative (choices)
-Loot and other rewards
The thing that established all these attributes and thus can be viewed as the "pure RPG" would be the tabletop RPG and they are usually treated as their own medium (though some would argue they belong under the umbrella of "tabletop gaming", but that is pretty nebulous.)
However, you can take some of these elements out of the context of a pure RPG and you can put them into other interactive media (read: vidya games). The two aspects most often taken out are the advancement systems ("RPG elements") and the player agency (cue "Your choices shape the story and the game-world!" PR babble). Just because these elements can give any other game the trappings of RPGs doesn't make pure tabletop RPGs any less valid as their own medium.
In contrast, a pure Visual Novel has a number of very specific trappings.
-Has an audiovisual aspect (in contrast to books or pure text-based adventure games)
-Has no traditional gameplay elements
-Tells a story using the ADV (text-box at the bottom, 2D full-body sprites (tachies) at the front) or NVL (the transparent text-box covers the entire screen, the graphics are behind it) format
-Uses text exclusively to tell its story (the graphics and BGM are only there for illustration and setting the mood)
-Uses consistent narration
Thus a pure Visual Novel would be something like Fate/Stay Night, a title with audiovisuals, no gameplay, NVL presentation, text based storytelling and consistent narration.
However, you can take some of these element out of the context of a pure VN and you can put them into different interactive media. The one that is the most common is the ADV presentation, which is a very straightforward and cost-effective format when it comes to display dialog, and thus a lot of JRPGs use it (eg: the Persona series).
However, most of the time these are only considered VN elements of convenience, and it is much more common for things to go the other way when gameplay elements from video games get injected into VNs (usually JRPG battles and leveling and turn based combat/strategy). However, the final deciding factors that decides whether it's a game with VN trappings or a VN with gameplay elements is always the presence of consistent narration and the VN/gameplay ratio.
In the end though, just because there are hybrid games with VN elements in them doesn't mean that the pure VNs are any less valid as their own medium.
And with that I rest my case for why VNs can be considered both a separate medium and a video game genere depending on the "purity" of the defining elements present.
To examine how that works, let's look at another thing that can be both a medium and a genre: RPGs.
An pure RPG has a number of very specific trappings.
-Focuses on a character/set of characters and their acts and deeds
-Character advancement (levels, ability points, skill training, etc.)
-Provides a narrative, with goals and rewards (quests)
-Gives the audience agency when forming the narrative (choices)
-Loot and other rewards
The thing that established all these attributes and thus can be viewed as the "pure RPG" would be the tabletop RPG and they are usually treated as their own medium (though some would argue they belong under the umbrella of "tabletop gaming", but that is pretty nebulous.)
However, you can take some of these elements out of the context of a pure RPG and you can put them into other interactive media (read: vidya games). The two aspects most often taken out are the advancement systems ("RPG elements") and the player agency (cue "Your choices shape the story and the game-world!" PR babble). Just because these elements can give any other game the trappings of RPGs doesn't make pure tabletop RPGs any less valid as their own medium.
In contrast, a pure Visual Novel has a number of very specific trappings.
-Has an audiovisual aspect (in contrast to books or pure text-based adventure games)
-Has no traditional gameplay elements
-Tells a story using the ADV (text-box at the bottom, 2D full-body sprites (tachies) at the front) or NVL (the transparent text-box covers the entire screen, the graphics are behind it) format
-Uses text exclusively to tell its story (the graphics and BGM are only there for illustration and setting the mood)
-Uses consistent narration
Thus a pure Visual Novel would be something like Fate/Stay Night, a title with audiovisuals, no gameplay, NVL presentation, text based storytelling and consistent narration.
However, you can take some of these element out of the context of a pure VN and you can put them into different interactive media. The one that is the most common is the ADV presentation, which is a very straightforward and cost-effective format when it comes to display dialog, and thus a lot of JRPGs use it (eg: the Persona series).
However, most of the time these are only considered VN elements of convenience, and it is much more common for things to go the other way when gameplay elements from video games get injected into VNs (usually JRPG battles and leveling and turn based combat/strategy). However, the final deciding factors that decides whether it's a game with VN trappings or a VN with gameplay elements is always the presence of consistent narration and the VN/gameplay ratio.
In the end though, just because there are hybrid games with VN elements in them doesn't mean that the pure VNs are any less valid as their own medium.
And with that I rest my case for why VNs can be considered both a separate medium and a video game genere depending on the "purity" of the defining elements present.