Ohh, this is a difficult question, but I'll try to help. Beware - it's going to be long.
For the sibling part - it usually refers to swords which were made by the same bladesmith. They usually have similar motifs in their clothes, for example - in the anime you can see
Yagen and
Atsushi, who were made by Toushirou Yoshimitsu (which is why they are called Toushirou, and most of the swords made by him bear his name). All these tantous refers to each other as siblings (we have
Ichigo Hitofuri as well, and since he's a tachi, he's like an "older" brother). Toushirou Yoshimitsu was a part of the Awataguchi school, so
Nakigitsune, despite actually being made by Yoshimitsu's father, is also considered a relative to the Toushirou swords, and his clothes are also in line with the Toushirou's design.
As for the old masters, it’s super difficult to explain in detail regarding each sword because some swords passed multiple hands and were owned by different people, not to mention how some of the records are not completely reliable. Oda Nobunaga was a collector of Mitsutada’s swords, was
Shokudaikiri Mitsutada a sword in his collection? We can’t say for certain 🤷♀️. The line is veryyy blurred here, as mentioned before for Shokudaikiri - he was a sword of Date Masamune, and usually for his Date group we have
Taikogane Sadamune (also owned by Date Masamune at some point in his life),
Ookurikara (which might’ve been owned by Date Masamune’s son and not he himself), and
Tsurumaru Kuninaga (which joined the Date clan much, much later). Some grouping aren't solely based on the same old owner, but also a faction - a good example would be the Shinsengumi swords, which were owned by memebers of the Shinsengumi and thus are familiar with each other < I'm not going to name them here because it'll turn out to be a long list and I don't think anyone wanna read that lol.
Honestly, understanding that really requires knowing the history of the certain sword, unfortunately, and also understanding the mindset of the creators since, again, some ownerships are based on rumors and speculations. The amount of characters doesn't help at all because you'd have characters being in quite a few groups, all depends on who made them or who owned them :,)
However, for this series it seems the focus is on the Oda Nobunaga's swords, which would be Yagen Toushirou, Heshikiri Hasebe, Souza Samonji and Yukimitsu Fudou. Oda Nobunaga is usually depicted as a questionable figure in tourabu (and some media in general, I guess, depends on what you consume), so most of the swords aren't very fond of him or want to talk about him.
I've added links for the characters that aren't the main focus of the anime so hopefully it won't be too confusing. If you do have any specific questions, feel free to ask. I don't want to ramble too much lol, but I still somewhat remember the relationships between the characters that were released up until 2018, that's when I stopped following the game altogether.