Got into the part of your post re: karate sparring styles and neglected this point. While traditional Okinawan kobudo (sort of dying out post WWll) has been preserved to a great extent by karate largely thru the efforts of Taira Shinken in the mid 1950's and often practiced in parallel to it, IMO it's not really an inherent part of karate, but more of an add on - perhaps seen as an adopted child. This is the background as I know it.
The progenitors of karate (Shuri-te) were professional warriors such as Matsumura who in addition to empty hand combat were trained in several weapons including sword (not a part of Okinawan kobudo), bo and sai (from his years in China). Taira Shinken learned kobudo from a couple of Matsumura's students. Other weapons such as kama, tonfa, nunchaku and eku (oar) were used by farmers and fishermen with no formal empty hand combat training, but we can't know what that originally looked like. Modern kobudo includes both these lineages.
Nowadays kobudo has a lot in common with karate fundamentals and largely studied by those with karate training. But (I believe) can be studied as a separate art without prior karate training although those fundamentals must still be taught. There are weapon movements which are unique and not found in karate. There are three major schools/styles of kobudo with a full kobudo curriculum and belt system: Ryuuku and Matayoshi (both stemming from Matsumura) and Yamani (whose lineage I don't know beyond Master Agena).
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This is the hand forged Agena sai made by 9th dan Peter Carbone. They were formerly produced by several generations of the Miyahara family. With Hanshi Carbone's recent retirement from the craft, they are no longer made. Several top Okinawan masters own a pair. Mine are just like this - Sai that Bushi Matsumura himself would have loved.