feat: add federation badges to mobile surfaces

Globe/amber badge on federated space icons, @domain on federated
DM users, home instance on the You screen profile card.

packages/web/src/components/layout/MobileDmsScreen.tsx

@@ -9,6 +9,7 @@ import { Avatar } from '../ui/Avatar';
 import { Mascot } from '../ui/Mascot';
 import { resolveAssetUrl } from '../../utils/assetUrls';
 import { useNavigate } from 'react-router-dom';
+import { parseFederatedUsername } from '../../utils/identity';
 
 export function MobileDmsScreen() {
   const pushMobileScreen = useUIStore((s) => s.pushMobileScreen);
@@ -195,6 +196,13 @@ export function MobileDmsScreen() {
                     </span>
                   )}
                 </div>
+                {(() => {
+                  const mainUser = otherMembers[0];
+                  if (!mainUser) return null;
+                  const { domain } = parseFederatedUsername(mainUser.username);
+                  if (!domain) return null;
+                  return <div className="text-[10px] leading-[1.3] text-txt-tertiary truncate opacity-60">@{domain}</div>;
+                })()}
                 {preview && (
                   <p className={`text-xs truncate mt-0.5 ${isUnread ? 'text-txt-secondary font-medium' : 'text-txt-tertiary'}`}>
                     {previewSender && previewSender.id !== authUser?.id

packages/web/src/components/layout/MobileSpacesScreen.tsx

@@ -13,6 +13,7 @@ import type { Channel } from '@backspace/shared';
 import { Mascot } from '../ui/Mascot';
 import { ConfirmDialog } from '../ui/ConfirmDialog';
 import { TransferOwnershipModal } from '../modals/TransferOwnershipModal';
+import { useInstanceStore } from '../../stores/instanceStore';
 
 export function MobileSpacesScreen() {
   const spaces = useSpaceStore((s) => s.spaces);
@@ -466,6 +467,24 @@ export function MobileSpacesScreen() {
                   </span>
                 )}
               </button>
+              {(() => {
+                const origin = (space as TaggedSpace)._instanceOrigin;
+                if (!origin) return null;
+                const instances = useInstanceStore.getState().instances;
+                const inst = instances.find(i => i.origin === origin);
+                const isDisconnected = inst ? !inst.connected : false;
+                return (
+                  <div className="absolute -bottom-0.5 -right-0.5 w-[14px] h-[14px] rounded-full bg-surface-base flex items-center justify-center">
+                    {isDisconnected ? (
+                      <div className="w-[8px] h-[8px] rounded-full bg-accent-amber" />
+                    ) : (
+                      <svg width="10" height="10" viewBox="0 0 24 24" fill="currentColor" className="text-txt-tertiary/80">
+                        <path d="M12 2C6.48 2 2 6.48 2 12s4.48 10 10 10 10-4.48 10-10S17.52 2 12 2zm-1 17.93c-3.95-.49-7-3.85-7-7.93 0-.62.08-1.21.21-1.79L9 15v1c0 1.1.9 2 2 2v1.93zm6.9-2.54c-.26-.81-1-1.39-1.9-1.39h-1v-3c0-.55-.45-1-1-1H8v-2h2c.55 0 1-.45 1-1V7h2c1.1 0 2-.9 2-2v-.41c2.93 1.19 5 4.06 5 7.41 0 2.08-.8 3.97-2.1 5.39z" />
+                      </svg>
+                    )}
+                  </div>
+                );
+              })()}
             </div>
           );
         })}

packages/web/src/components/layout/MobileYouScreen.tsx

@@ -3,6 +3,7 @@ import { useUIStore } from '../../stores/uiStore';
 import { useAuthStore } from '../../stores/authStore';
 import { Avatar } from '../ui/Avatar';
 import { ConfirmDialog } from '../ui/ConfirmDialog';
+import { parseFederatedUsername } from '../../utils/identity';
 
 export function MobileYouScreen() {
   const pushMobileScreen = useUIStore((s) => s.pushMobileScreen);
@@ -99,6 +100,11 @@ export function MobileYouScreen() {
             {user.displayName ?? user.username}
           </h2>
           <p className="text-sm text-txt-secondary">@{user.username}</p>
+          {(() => {
+            const { domain } = parseFederatedUsername(user.username);
+            if (!domain) return null;
+            return <div className="text-[10px] leading-[1.3] text-txt-tertiary opacity-60">Home instance: {domain}</div>;
+          })()}
           {user.customStatus && (
             <p className="text-sm text-txt-secondary mt-1">{user.customStatus}</p>
           )}