Replication is a Server → Client process. Actions on the client do not replicate up.
Outside of general movement, actions that effect world game play need to happen on the server.
e.g. Doors, Loot management (Add, Drop, Use), Health, Stamina etc.
Client inputs the action. Client checks if it would be applicable locally. If so, RPC the server and have it check, then do.
For inventory you want the server to pickup and add the item to inventory.
Inventory actor needs to be set to replicates.
Inventory variables need to set to replicates.