First of all, the way you're making keybinds is horrible, here's an example of how I make keybinds in my mod.
Your problem seems to be that you aren't SYNCING your capability to the CLIENT. Capabilities are stored only on the server by default, check out this example of how I sync capabilities in my mod (you also have to sync on the player logging in, changing dimensiom, leaving the end and respawning). Also, why do you have a public static class in you CapabilityHandler class, it serves no purpose at all, just remove it.