feat(frontend): relay discoverability toggle, sign-up disclosure, offline badge

- setRelayDiscoverable IPC wrapper in tauri.ts
- relay_discoverable in defaultSettings + toggleRelayDiscoverable function
- Privacy settings: discoverable on relay toggle
- Sign-up: disclosure text about relay username storage
- User directory: WifiOff badge for relay-only (offline) peers
- Improved empty state hint text

Generated with [Claude Code](https://claude.ai/code)
via [Happy](https://happy.engineering)

Co-Authored-By: Claude <noreply@anthropic.com>
Co-Authored-By: Happy <yesreply@happy.engineering>

src/components/auth/SignUpScreen.tsx

@@ -167,6 +167,11 @@ const SignUpScreen: Component<SignUpScreenProps> = (props) => {
               an ed25519 keypair will be generated and stored locally on your
               device
             </p>
+            <p class="text-[11px] font-mono text-white/30 text-center mt-2 leading-relaxed">
+              your username will be stored on the relay server so others can
+              find you even when you're offline.{" "}
+              <span class="text-white/40">you can turn this off in settings.</span>
+            </p>
           </div>
         </Match>
       </Switch>

src/components/directory/UserDirectoryModal.tsx

@@ -16,6 +16,7 @@ import {
   Users,
   Copy,
   Check,
+  WifiOff,
 } from "lucide-solid";
 import Avatar from "../common/Avatar";
 import Button from "../common/Button";
@@ -263,7 +264,9 @@ const UserDirectoryModal: Component<UserDirectoryModalProps> = (props) => {
                     <p class="text-[14px] text-white/20">
                       {activeTab() === "friends"
                         ? "add friends from the all peers tab"
-                        : "peers will appear as you join communities"}
+                        : searchQuery().trim().length > 0
+                          ? "try searching by peer id or check your relay connection"
+                          : "peers will appear as you join communities or search by name"}
                     </p>
                   </div>
                 }
@@ -283,6 +286,12 @@ const UserDirectoryModal: Component<UserDirectoryModalProps> = (props) => {
                                 friend
                               </span>
                             </Show>
+                            <Show when={!peer.public_key}>
+                              <span class="flex items-center gap-1 text-[10px] font-mono uppercase tracking-[0.05em] text-white/30 px-1.5 py-0.5 border border-white/10 shrink-0">
+                                <WifiOff size={8} />
+                                offline
+                              </span>
+                            </Show>
                           </div>
                           <Show when={peer.bio}>
                             <p class="text-[13px] text-white/40 truncate">

src/components/settings/SettingsModal.tsx

@@ -21,11 +21,12 @@ import {
   toggleMessagePreview,
   toggleShowOnlineStatus,
   toggleAllowDMsFromAnyone,
+  toggleRelayDiscoverable,
   setMessageDisplay,
   setFontSize,
 } from "../../stores/settings";
 import { identity, updateIdentity } from "../../stores/identity";
-import { updateProfile } from "../../lib/tauri";
+import { updateProfile, setRelayDiscoverable } from "../../lib/tauri";
 import type { UserStatus } from "../../lib/types";
 import Avatar from "../common/Avatar";
 import Button from "../common/Button";
@@ -378,6 +379,19 @@ const PrivacySection: Component<{
         checked={current().allow_dms_from_anyone}
         onChange={toggleAllowDMsFromAnyone}
       />
+      <ToggleRow
+        label="discoverable on relay"
+        description="lets others find you by username even when you're offline. turning this off removes your profile from the relay index."
+        checked={current().relay_discoverable ?? true}
+        onChange={async () => {
+          toggleRelayDiscoverable();
+          try {
+            await setRelayDiscoverable(!current().relay_discoverable);
+          } catch (e) {
+            console.error("failed to set relay discoverable:", e);
+          }
+        }}
+      />
 
       {/* danger zone */}
       <div class="mt-8 pt-6 border-t border-red-500/20">

src/lib/tauri.ts

@@ -296,6 +296,10 @@ export async function discoverGlobalPeers(): Promise<void> {
   return invoke("discover_global_peers");
 }
 
+export async function setRelayDiscoverable(enabled: boolean): Promise<void> {
+  return invoke("set_relay_discoverable", { enabled });
+}
+
 export async function setRelayAddress(relayAddr: string): Promise<void> {
   return invoke("set_relay_address", { relayAddr });
 }

src/stores/settings.ts

@@ -11,6 +11,7 @@ const defaultSettings: UserSettings = {
   enable_message_preview: true,
   show_online_status: true,
   allow_dms_from_anyone: true,
+  relay_discoverable: true,
   message_display: "cozy",
   font_size: "default",
 };
@@ -86,6 +87,13 @@ export function toggleAllowDMsFromAnyone() {
   }));
 }
 
+export function toggleRelayDiscoverable() {
+  setSettings((prev) => ({
+    ...prev,
+    relay_discoverable: !prev.relay_discoverable,
+  }));
+}
+
 export function setMessageDisplay(mode: "cozy" | "compact") {
   updateSettings({ message_display: mode });
 }