I was trolling the internet and from what I understand it means using the sheath of your sword as a blunt weapon when the sword was too unwieldy to use i.e. when you are too close to bring your sword up.

I've never come across any record claiming this nor have I seen any school of kenjutsu teaching this. In fact, the katana was most likely developed as a consequence of Japanese melee evolving to favor closer and faster engagements. Before the katana's popularity, most samurai used tachi, which had considerably longer hilts and blades than katana.

Over time, katana were developed to be swift and maneuverable weapons. For this reason, katana were always worn with the blade side up so a swordsman could quickly draw his sword and cut down an opponent in a single, rapid motion. Low response time and efficiency of movement was so important in Japanese fencing that the samurai developed an entire discipline around it, essentially the art of the sword quick draw.

Since the katana was designed to be the much more manageable version of the tachi, it wouldn't make any sense for anyone to use the scabbard for combat. Even as a weapon of desperation, the saya was an awful choice. They were hollow and light which would have made them ineffective even against an unarmored opponent, much less a fully equipped soldier, and they were made of lacquered wood or polished bone. Materials like that stand no chance against proper instruments of war forged from steel and heavy oak. In fact, it would have been much more practical for a samurai to fight an opponent unarmed rather than using a saya! I'll explain this in my next response below.

It also seems that using a mix of martial arts to bring yourself closer to the enemy to deny them the use of their weapons was a big part of it as well.

This is true and it's the reason why jiujitsu was developed. Though striking arts were practiced in Okinawa for hundreds of years, they did not gain popularity in Japan until the 20th century. Punching and kicking wasn't very useful on a medieval Japanese battlefield since everyone was armed and armored. However, throwing, joint locking, trapping, choking, grappling, and disarming all worked perfectly fine.

However, though jiujitsu was an important part of warfare, it was still a last resort. It's something you busted out when you were caught with your pants down. The goal was to disarm the opponent until you could find a proper weapon.

I don't really know what you're talking about. It seems like you are referencing some specific motion or movement in combat. But I would like to clarify that a samurai would most likely be using a spear or a bow in battle, rather than a katana. Or am I missing your point?