Save/Load Animation State of Instantiated Prefabs

My game is made up of a single scene. At the start of the game lots (>100) of the same prefab are instantiated into the game. While playing the player is able to change the animation state of each of these prefabs separately.

I would like the player to be able to save the animation state of every one of these prefabs in the scene, in some sort of save file (of which there would be multiple save files), to then later be loaded when the payer decides to. (All from the UI)

I've read a fair bit on this, including PlayerPrefs and Serialization, but I am a bit lost with how to go about doing it and what would be the best way? A point in the right direction would be greatly appreciated. Thanks!