Three uses, one blade
You find the glaive in Advanced Research during Escape the Assembly. It is not a late upgrade. From that point the published uses are: strike or hit a switch, recall the blade to your hand, and Fold yourself to where the blade is. Players describe a chain — boomerang throw, grapple, dive — as the way across several gaps. Hurl is the long throw that leaves the blade in place so a distant switch can fire.
The confusion at Spillway, at the teaching room, and at any “throw the rock” switch is almost always throw versus hurl. If the blade comes home, you threw. If it stays, you hurled. Recall brings a hurled blade back. The Assembly tutorial wants the returning throw. The developer said they plan to make that room clearer.
What is still a lesson, not a list
Twin Sight, Nexus, Overclock, and Super Glaive have their own Revelation flags (LINKINGROOM_LEARNED, OVERCLOCK_LEARNED, SUPERGLAIVE_LEARNED, and the warp and unbinding flags). I can name the flags. I cannot publish a step-by-step unlock order I have not confirmed in the UI. The lessons appear when you do the thing, because the abilities are already on you. Glaive grapple is one of the four hidden moves (MT_GLAIVEGRAPPLE), alongside slide jump, fast fall, and sprint.
Show the sourced solution
Short throw returns. Hurl stays until Recall. Folding pulls you to the blade. Tetsa’s check is Recall. The Assembly teaching room wants the short throw.