Using a multimeter, I checked the continuity of the aluminum sheathing against any of the conductor wires (black/white/green) and there is no continuity to any of them
And then, when I wired the 3 conductors to a plug and plugged it in an outlet (which is connected to main panel), I tested the continuity again and the sheathing has continuity to the ground wire and neutral (green and white).
Photos for reference. Note that the other end of the wire is terminated (not connected to anything)
That’s normal. The green wire is insulated and it never connects to the metal covering of the cable inside the cable.
It’s your responsibility to ground the metal cover. Generally that happens by clamping it to a metal junction box that is grounded.
In the second picture, the continuity to ground is probably due to the cover touching some grounded metal outside the photographed area. You’d see the same continuity between the shell and ground if you unplugged the plug and put your black meter probe in the ground pin hole directly.