Connect to the real Nexa backend, replacing the mock lock toggle

Adds the wire-protocol WebSocket client (ws-client.ts) and the REST
auth flow (backend-client.ts) against the now-live backend, using a
locally-generated ed25519 keypair (identity.ts) as a stand-in wallet
signer until real wallet-extension integration is built.

lock-state.ts's setLockState is now applyLockState, called only by
the WS client on an incoming lock_state message -- the backend is
the sole source of truth for lock state, so there's no other writer
anymore. The popup's dev mock controls are replaced with a live
connection-status + lock-state display.

Verified end-to-end against the real backend (nonce -> verify -> /me
-> ws lock_state) using the same tweetnacl/bs58 libs shipped in the
extension.

Co-Authored-By: Claude Sonnet 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01YXiHuScXrjxBh7yFGAPq3B

src/entrypoints/popup/style.css

@@ -19,6 +19,35 @@ header .subtitle {
   opacity: 0.65;
 }
 
+.connection {
+  margin-bottom: 10px;
+  opacity: 0.75;
+  display: flex;
+  align-items: center;
+  gap: 6px;
+}
+
+.connection-dot {
+  width: 8px;
+  height: 8px;
+  border-radius: 50%;
+  display: inline-block;
+  background: currentColor;
+}
+
+.connection-connecting {
+  color: #ca8a04;
+}
+
+.connection-connected {
+  color: #16a34a;
+}
+
+.connection-disconnected,
+.connection-auth-error {
+  color: #dc2626;
+}
+
 .status {
   margin-bottom: 16px;
 }
@@ -50,37 +79,6 @@ header .subtitle {
   opacity: 0.65;
 }
 
-.dev-controls {
-  border-top: 1px solid rgba(128, 128, 128, 0.25);
-  padding-top: 12px;
-}
-
-.dev-controls h2 {
-  margin: 0 0 4px;
-  font-size: 12px;
-  text-transform: uppercase;
-  letter-spacing: 0.04em;
-  opacity: 0.65;
-}
-
-.dev-controls .hint {
-  margin: 0 0 10px;
-  opacity: 0.6;
-}
-
-.field {
-  display: flex;
-  align-items: center;
-  justify-content: space-between;
-  gap: 8px;
-  margin-bottom: 8px;
-}
-
-.field input[type='text'] {
-  flex: 1;
-  min-width: 0;
-}
-
 .thresholds-link {
   display: block;
   margin-top: 14px;