The writers are pretty inconsistent about which swords exist in Touken Ranbu’s historical timeline.
For example, consider the Sanjou school. Outside of Mikazuki Munechika, who has a proven existence as the sword forged by Sanjou Munechika and currently resides in Tokyo's Nation Museum, the existence of every other sword can be disputed, as while there are many swords named Kogitsunemaru in real life, none of them can explicitly claimed to be the famous one forged by Sanjou Munechika, making it likely that the sword is just a legend. Similarly, the existence of Ishikimaru appears to be made up of many accounts of swords named Ishikirimaru, none of which have explicit ties to Sanjou Munechika. Despite this, unlike Imanotsurugi and Iwatooshi after their Kiwame training, the possibility that either or both of them are not real is never mentioned in their stories, with Kogitsunemaru even traveling back in time to assist Munechika in forging his blade. Perhaps they didn't want to be redundant or make Mikazuki the only true Sanjou sword in the game?
And, while Kogitsunemaru is an obvious choice for inclusion in the game because he's probably Sanjou Munechika's second most famous sword after Mikazuki Munechika himself, real or not, it also makes you wonder why the writers chose so many Sanjou swords with flimsy foundations in reality to add to the game when there are several genuine Sanjou swords that could have been included, such as Ebina-Kokaji, a Tantou, and Takanosu Munechika, a Wakizashi.
What makes certain swords brothers, let alone family? The most likely answer is being forged by the same smith, but Sanjō school, Gō school, Kagemitsu and Nagamitsu swords, etc. share smiths but don't seem to be family, while Tarōtachi and Jirōtachi were forged by different people but are brothers.
The best answer is most likely that it comes down to a Touken Danshi's perception. In the first place, Touken Danshi being "brothers" has no basis in reality, as they are not blood related and are simply objects brought to life and given human shape. However, if they build a close friendship with a Touken Danshi from the same or a related school, they can declare that they feel like siblings, and therefore they are, because they feel like they are. As we've seen in the spin-offs and, eventually, the browser game, the Sanjou swords don't have a familial, let alone close dynamic with one another, and are formal with each other, so they naturally wouldn't claim to be a family. The Awataguchi swords, on the other hand, are shown to be quite close, and most of them are like children, so they would naturally perceive the mature Ichigo Hitofuri as their older brother, or at least as an older brotherly figure. It also probably helped that he's the only Tachi from their school.
In shorter words, whether or not swords are siblings depends entirely on their relationship dynamics with each other and their perception. They can just decide whether or not they're siblings based on that.
What factors influence the physical age of the Touken Danshi? Over the years, it has stopped being consistent due to the number of exceptions introduced in each sword-type and even some exceptions that have existed since launch, such as Kashuu Kiyomitsu and Yamato-no-Kami Yasusada looking and acting like teenagers despite the vast majority of Uchigatana resembling young adults. Even Odachi had Hotarumaru from the start, who inexplicably resembles a Tantou despite the size of his sword.
If the lore of Honebami and Namazuo is any guide, shortening swords likely influences how the swords appear in human form, possibly in terms of physical age as well, as both were previously Naginata. Chatannakiri is also said to resemble a Tantou due to being overly sharpened over the years. Having said that, Nikkari Aoe, who was also shortened, looks like a short young adult rather than a teenager like Honebami and Namazuo, leading to more questions.
Despite being the oldest of the Touken Danshi at the time of his release, Kogarasumaru was the first Tachi introduced who looks more like a Tantou in terms of physical age and is even mistaken for a child In-Universe. The reason for his physical age is never explicitly stated, though it could be attributed to the fact that his name is "Kogarasumaru," with the "Ko" in his name meaning "small." However, Kogitsunemaru, who has been in the game since its inception, also has the "small" Kanji in his name and appears to be a young adult. He even mentions that, contrary to his name, he is not small. After a while, you have to wonder if it's just the artist's choice to deviate rather than any lore basis.
After the revelation that Mikazuki Munechika and Tsurumaru Kuninaga are depicted as being close in nearly every major spin-offnote Hanamaru, Katsugeki (mentioned as formerly being partners in the final episode, Katsugeki collaboration with Granblue Fantasy has them interact more), stage play, Warriors, the musical. Only exception is the live actions movies since Tsurumaru isn’t a major character in those and only has a very brief cameo in the second. Heck, even Touken Camp has him hanging out with Mikazuki and Kogitsunemaru, fans started speculating as to whether there is some kind of unspoken guideline that all spin-offs follow mandating that they have a relationship, despite the fact that the two have no interactions or indication that they have a personal relationship in the browser game itself, or if every writer coincidentally decided to pair the two off based off of their history of being from related schools. It hasn't helped that none of the spin-offs ever clarify the relationship between the schools when they interact (at best, Tsurumaru mentions "Sanjou" in three different spin-offs but never elaborates on what he means or what it means to him, nor does he ever have any significant interactions or bonds with non-Mikazuki Sanjou's), leading to theories about why Mikazuki, in particular, is always so close to him. Maybe because they are both signature swords for their respective schools? There is also a real life theory that Tsurumaru was forged using Mikazuki as a reference due to how strikingly similar his sword looks to Mikazuki, so that could be another reason.
