What really surprises me is that with all the thinking and efforts that went into bow design - why did nobody invent my bow magazine earlier? It could have been done back then, easily.
Of course there was the Chu Ko Nu repeating crossbow, but that one had many flaws. Weak, totally inaccurate (unvaned bolts and awkward shooting position) and unreliable (gravity fed magazine).
Perhaps this is rather late for a reply, but I don't think you should brush off the Chu-ko-nu so lightly. Wikipedia references a handful of rather poor sources, and videos almost invariably show very weak versions. Chu-ko-nu were used on the battlefield over a very long period, so they couldn't have all been peasant dart shooters.
Composite recurve bows can be very energy efficient - a reproduction Manchu bow, with a draw weight of 82lbs at 32 inches draw length, can shoot an 80-gram arrow at 190 fps, with an energy of 135 joules.
Now, the composite recurve bows used in military Chu Ko Nu were probably somewhat less efficient than normal Manchu bows, but a reproduction of a European crossbow design used on battlefields shoots projectiles with 54 joules, and that kind of energy should be easily reachable even for a composite bow downsized to fit on a normal-sized crossbow. That kind of energy won't pierce armor, but it will cause serious injury to unarmored peasant levies or steppe nomads.
So, you can imagine a weapon that has the power of some medieval European crossbows, but can fire at least as fast as a skilled archer using a normal bow, due to the magazine and the mechanical advantage of the reloading lever. As far as accuracy goes, two veined-bolts can work in a magazine, as you've shown on your channel, and I can't imagine that Chinese engineers couldn't have figured it out as well.
Unfortunately, I don't think anyone's built a replica of a more powerful Chu-ko-nu, and tested it to see how it compares to other historical bows and crossbows. I think it would make for a very interesting Slingshot Channel video, if this kind of thing interests you. If you wanted to do it, instead of using a traditional composite recurve bow, which can be very hard and expensive to come by, you could use any bow of similar energy efficiency - I think fiberglass or fiberglass composite bows are the standard for people who practice traditional Asian archery today.
RE: bow magazine, I think that it just wouldn't have been useful for most historical practical uses of a bow. In hunting you generally want to kill with the first shot. In war, you generally don't want your men to waste their energy all at once, so you wouldn't want your archers to shoot as fast as possible, even if they could. There are some hints of ancient Persians using a tactic whereby archers would fire 5 volleys as fast as possible at the beginning of a battle, but that probably wasn't used often enough to make carrying around a dedicated magazine worthwhile.