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

package-lock.json

@@ -8,6 +8,10 @@
       "name": "nexa-extension",
       "version": "0.1.0",
       "hasInstallScript": true,
+      "dependencies": {
+        "bs58": "^6.0.0",
+        "tweetnacl": "^1.0.3"
+      },
       "devDependencies": {
         "typescript": "^7.0.2",
         "wxt": "^0.21.4"
@@ -1556,6 +1560,12 @@
         "url": "https://github.com/chalk/ansi-styles?sponsor=1"
       }
     },
+    "node_modules/base-x": {
+      "version": "5.0.1",
+      "resolved": "https://registry.npmjs.org/base-x/-/base-x-5.0.1.tgz",
+      "integrity": "sha512-M7uio8Zt++eg3jPj+rHMfCC+IuygQHHCOU+IYsVtik6FWjuYpVt/+MRKcgsAMHh8mMFAwnB+Bs+mTrFiXjMzKg==",
+      "license": "MIT"
+    },
     "node_modules/boolbase": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/boolbase/-/boolbase-2.0.0.tgz",
@@ -1570,6 +1580,15 @@
         "url": "https://github.com/sponsors/fb55"
       }
     },
+    "node_modules/bs58": {
+      "version": "6.0.0",
+      "resolved": "https://registry.npmjs.org/bs58/-/bs58-6.0.0.tgz",
+      "integrity": "sha512-PD0wEnEYg6ijszw/u8s+iI3H17cTymlrwkKhDhPZq+Sokl3AU4htyBFTjAeNAlCCmg0f53g6ih3jATyCKftTfw==",
+      "license": "MIT",
+      "dependencies": {
+        "base-x": "^5.0.0"
+      }
+    },
     "node_modules/c12": {
       "version": "3.3.4",
       "resolved": "https://registry.npmjs.org/c12/-/c12-3.3.4.tgz",
@@ -2732,6 +2751,12 @@
         "url": "https://github.com/sponsors/SuperchupuDev"
       }
     },
+    "node_modules/tweetnacl": {
+      "version": "1.0.3",
+      "resolved": "https://registry.npmjs.org/tweetnacl/-/tweetnacl-1.0.3.tgz",
+      "integrity": "sha512-6rt+RN7aOi1nGMyC4Xa5DdYiukl2UWCbcJft7YhxReBGQD7OAM8Pbxw6YMo4r2diNEA8FEmu32YOn9rhaiE5yw==",
+      "license": "Unlicense"
+    },
     "node_modules/typescript": {
       "version": "7.0.2",
       "resolved": "https://registry.npmjs.org/typescript/-/typescript-7.0.2.tgz",