I'm not sure if it's a highly popular genre specifically. It might have a niche following among those interested in medieval or royalty - themed stories.
I'm not entirely sure as I haven't experienced it directly. But generally, a visual novel often involves a story with characters and plotlines. Since it has 'kingsguard' in the title, it might be related to a group of guards in a king - like setting. And 'furry' could imply the presence of anthropomorphic animal characters.
It's highly unlikely that the characters in 'House of the Dragon' would actually watch fanfiction about themselves. Fanfiction exists in our world, created by fans for fans, and the characters in the show are fictional entities within their own fictional universe. They don't have access to the fan - created stories about them.
One great 'oc kingsguard fanfiction' could be one where the OC has a unique backstory that ties into the world of the Kingsguard in an unexpected way. For example, an OC who was once a street urchin but through a series of events becomes a part of the Kingsguard and has to learn the ways of honor and loyalty quickly.
Since I haven't played or read it, I can't say for sure. But if it follows the typical pattern of visual novels, there are likely to be a variety of interesting characters. Given the 'kingsguard' and 'furry' aspects, there could be brave guards with unique animal - like features and personalities.
One interesting plotline could be a Kingsguard member having to choose between loyalty to a tyrannical king and protecting the innocent. For example, if the king orders unjust executions, the Kingsguard might struggle with their oath.
Ser Jaime Lannister is often a popular character. His complex character arc in the original series makes him ripe for further exploration in fanfiction. His internal struggle between honor and family loyalty can be delved into more deeply.
Definitely not a true story. House of the Dragon is a work of imagination and creativity. It weaves a complex tale of power, politics, and dragons within a fictional realm.