I really like the addition you've made to the fight against the enemies because you don't know if the enemy is really fought effectively.

But after several intense fights against the enemy I realised that the downed enemies get in the unconscious state too fast.

For now unconscious enemies instantly switch from ragdoll to a "laying on their back"-position after a few seconds.
You only have to wait for a short moment for the switch. In my opinion that kills the immersion a little bit.

My suggestion:
No animation switch to the "laying on back"-position and keep the downed enemy in its final ragdoll stage. This would make it more difficult to distinguish if the enemy is killed or just unconscious.

Another suggestion:
If possible, integrate some active ragdoll unconscious state where the enemy is moving slowly (squirming) on the ground after ten or twenty seconds.