So what you could do is:
Enable the Add Curve : Extra Object addon, add a Curve > Curve Spirals > Archemedian, in the settings, play with the Turns, Radius Growth and Radius values, put the curve it on the cylinder, apply the rotation:
Display the normals to make sure that the direction is good, if it’s not the case right click > Switch Direction:
Extrude a bit the starting tip:
Create a plane, give it an Array and a Curve modifier, put it at the exact same position as the curve, move it so that it doesn’t coil for the moment:
Create some keyframe in order to animate the reel, the cylinder, also keyframe the scale of the spiral so that the reel pile on itself:
