in this class should I store only public information (eg number of enemies killed, player name, ping)? Or in this class I can save everything (health, amount of money, etc.)?
It seems to me that Epic Games intended the Player State to be an object that stores information related to the player as a real person, rather than a character in the game.
Therefore, it is not worth storing the amount of health or ammo in it.
For health it is better to use your Pawn class, and for ammunition - Weapon.
And to store other items it is better to create your own Inventory class.