Taking a wild stab.
There may be two problems.
The reason is the shift rod goes down to a lever that’s outside the case. The lever rotates a short shaft which moves the yoke controlling the movement of the friction disk back and forth across the shaft to control speed. I don’t see a spring anywhere in this group other than a small one up by the speed lever on the handlebars. There are holes for each end so probably not the spring you see loose.
Problem 1. The shift yoke came off the bearing assembly so the speed lever has no resistance. No spring involved. The shift yoke has two arms that fit over the bearing assembly arms. So that’s the easy to move shift lever.
The rod could be separated at the base housing but that would be obvious and you would see that.
Problem 2. The spring. The spring you see could be the tensioner for the drive plate. That spring tensions another yoke which is behind the drive plate. The yoke attaches to a second bearing assembly with arms that the yoke go over. A spring always pulls the yoke assembly so the drive plate does not touch the friction disk. When you push down the clutch that whole assembly gets pulled up to the friction disk. So the drive plate has a yoke that is pulled away by the spring and may be the one you see. The other spring in there is over a rod so would not flop around or be loose.
How the spring attaches:
That spring attaches to one arm of the yoke. One side of the yoke has a hole. When the yoke is pointed to the ground the spring is in the hole and at a right angle to the yoke arm, pointed toward the blower housing. Put the spring in and hold it 90 to the yoke and you’ll find the attachment point. That may be a place on the back of the bucket.
The only other spring in the tractor drive is on the pulley tensioner and it should be obvious where the spring attaches so probably not that spring.
