Perhaps it provides a connection to the character's spiritual energy. The forehead is often seen as a spiritual center in some cultures. In the context of the fanfic, the busoshoku haki coating on the forehead could strengthen the character's link to their inner power, allowing them to tap into reserves of strength they didn't know they had. This could also enhance their ability to read the intentions of others, as if the haki on the forehead acts as an antenna for detecting the energy of those around them.
Perhaps Naruto discovered a hidden power within himself that was similar to Busoshoku Haki. In the fanfic, the author might have created a new backstory for Naruto where his Uzumaki heritage had some latent abilities that could be manifested as Haki - like powers. So, he just had to figure out how to use it on his swords.
He might become more confident. Knowing he has this extra layer of protection and power on his forehead gives him a boost in self - assurance. He may be more likely to take risks in battles or challenges.
One advantage would be increased durability. The Busoshoku Haki would make his swords harder and more resistant to damage. So, when he's in a tough fight against strong opponents, his swords won't break easily.
The fanfic could center around a group of characters. One of them is coated in invisible haki and has to protect the others from an unseen threat. The haki could act as a shield as well as a means of camouflage. It could also be a story of self - discovery, as the character learns more about the extent of their haki power and how it can be used not just for combat but also for stealthy exploration.
It could be a young and inexperienced warrior. They start off not knowing much about their haki ability but as the story progresses, they learn to master it. For example, a novice swordsman who discovers they can coat their sword and themselves in invisible haki, which gives them an edge in battles.
Coating his swords in Haki in the fanfic would change Naruto's combat abilities a great deal. Haki gives an extra layer of power. It could potentially make his swords more durable, so he doesn't have to worry about them breaking during intense battles. Also, it could add a new element to his fighting style. Since Naruto is known for his ninjutsu, adding swordsmanship with Haki - enhanced blades could make him a more versatile fighter. He could combine his Haki - powered sword strikes with his shadow clone jutsu, for instance, sending clones to attack while he uses the swords to fend off counterattacks.
In fanfic, 'coating his forehead in haki' might be a way to show the character is preparing for combat or enhancing their defense. Haki in some fictional universes is a form of spiritual energy. By coating the forehead, which is a vulnerable area, the character could be trying to protect themselves from attacks, especially those aimed at the head or face.
One possible plot could be a young swordsman discovers his sword has the ability to be coated with invisible haki. He then uses this unique skill to fight against powerful enemies in a world filled with magic and mystery. Maybe he starts as an underdog in a tournament but gradually rises to the top with his sword's special power.
In a fanfic, the character may also start to act more intimidating. The visible display of haki on the forehead can be a sign to opponents that the character is not to be trifled with. This could cause enemies to be more cautious around them, and the character could use this to their advantage, perhaps by bluffing or making opponents second - guess their moves.