Unity Static Singleton JSON Serialisation
Here are my observations after a quick review:

First of all your class is not a thread-safe singleton.

Please read Jon Skeet's guidance how to implement is properly.


As I understand you would like to implement a Memento pattern in C#.

There are a couple of good samples how to implement it properly: 1, 2, 3
BTW you can also use the Solid nuget package as well


Sorry but your naming is terrible, please try to follow some guideline, like:

Name your functions / methods in a way that they start with a verb, for example: SaveState, RestoreState
Name Your classes/ structs in a way that they are nouns (w/o adjective), for example: PlayerState,PortablePlayerState