feat(activity): show the current activity on the profile card

The activity pipeline was already complete end to end — Activity type, store,
WS broadcast, server validation, presence relay, and an ActivityCard used by
four list surfaces — but the profile card rendered none of it, which is the
'Listening to Spotify' block the design calls for.

Add ProfileActivity: richer than ActivityCard because the card has room for
artwork, track and artist, so it reads details/state/assets. All optional, so
it degrades to the bare name that today's process-based detector supplies.

Also scheme-check activity image assets server-side. activity.url was already
restricted to http(s) but assets.largeImage/smallImage were only length-checked
— an asymmetry that was harmless while nothing rendered them, and is not once
they become <img src>: a client could point them at a host it controls and
harvest the IP of everyone opening that profile.

packages/web/src/components/modals/UserProfileModal.tsx

@@ -3,6 +3,8 @@ import { useNavigate } from 'react-router-dom';
 import ReactMarkdown from 'react-markdown';
 import type { User } from '@backspace/shared';
 import { Avatar } from '../ui/Avatar';
+import { ProfileActivity } from '../ui/ProfileActivity';
+import { useActivityStore } from '../../stores/activityStore';
 import { Username } from '../ui/Username';
 import { useUIStore } from '../../stores/uiStore';
 import { useSpaceStore, getApiForOrigin, resolveUserOrigin } from '../../stores/spaceStore';
@@ -149,6 +151,13 @@ export function UserProfileModal() {
 
   // Banner — use correct API client for remote users
   const profileApi = getApiForOrigin(userOrigin);
+  // Keyed by home id, matching every other activity consumer (ActivityPanel,
+  // MemberSidebar), so federated users resolve to the same record. The `?? []`
+  // stays OUTSIDE the selector: building it inside would hand zustand a fresh
+  // array reference every render and spin.
+  const activityList = useActivityStore((s) => s.userActivities.get(user.homeUserId ?? user.id));
+  const activities = activityList ?? [];
+
   const bannerSrc = user.banner
     ? (user.banner.startsWith('http') ? user.banner : profileApi.uploads.url(user.banner))
     : null;
@@ -353,6 +362,9 @@ export function UserProfileModal() {
                 </div>
               )}
 
+              {/* Current activity — the "Listening to Spotify" block */}
+              <ProfileActivity activities={activities} />
+
               {/* Member Since */}
               <div>
                 <span className="text-[11px] uppercase tracking-wide font-semibold text-txt-tertiary">

packages/web/src/components/ui/ProfileActivity.tsx

@@ -0,0 +1,106 @@
+import { useEffect, useState } from 'react';
+import type { Activity } from '@backspace/shared';
+import { getPrimaryActivity } from '@backspace/shared/src/activities.js';
+
+interface ProfileActivityProps {
+  activities: Activity[];
+}
+
+const VERB: Record<Activity['type'], string> = {
+  playing: 'Playing',
+  listening: 'Listening to',
+  watching: 'Watching',
+  streaming: 'Streaming',
+  custom: '',
+};
+
+function formatClock(ms: number): string {
+  const total = Math.max(0, Math.floor(ms / 1000));
+  const minutes = Math.floor(total / 60);
+  const seconds = total % 60;
+  const hours = Math.floor(minutes / 60);
+  if (hours > 0) return `${hours}:${String(minutes % 60).padStart(2, '0')}:${String(seconds).padStart(2, '0')}`;
+  return `${minutes}:${String(seconds).padStart(2, '0')}`;
+}
+
+/**
+ * The activity block on the profile card — the "Listening to Spotify" panel.
+ *
+ * Deliberately richer than `ActivityCard` (which renders name + elapsed for
+ * compact list rows): here there is room for the artwork, the track and the
+ * artist, so it reads `details`, `state` and `assets` too. Every one of those
+ * is optional and the block degrades to just the name, which is all today's
+ * process-based detector supplies — the extra fields are what a Spotify
+ * producer would fill in.
+ */
+export function ProfileActivity({ activities }: ProfileActivityProps) {
+  const primary = getPrimaryActivity(activities);
+  const start = primary?.timestamps?.start;
+  const end = primary?.timestamps?.end;
+
+  // Re-render once a second only while there is a clock to advance.
+  const [now, setNow] = useState(() => Date.now());
+  useEffect(() => {
+    if (!start) return;
+    const id = setInterval(() => setNow(Date.now()), 1000);
+    return () => clearInterval(id);
+  }, [start]);
+
+  if (!primary || primary.type === 'custom') return null;
+
+  const elapsed = start ? now - start : 0;
+  const duration = start && end ? end - start : 0;
+  const progress = duration > 0 ? Math.min(Math.max(elapsed / duration, 0), 1) : 0;
+
+  // The server restricts asset images to http(s); this mirrors that so a
+  // record stored before that check cannot inject another scheme.
+  const art = primary.assets?.largeImage;
+  const artSrc = art && (art.startsWith('https://') || art.startsWith('http://')) ? art : null;
+
+  return (
+    <div>
+      <span className="text-[11px] uppercase tracking-wide font-semibold text-txt-tertiary">
+        {VERB[primary.type]} {primary.name}
+      </span>
+      <div className="mt-2 flex gap-3 rounded-lg bg-surface-elevated/40 p-2.5">
+        {artSrc && (
+          <img
+            src={artSrc}
+            alt={primary.assets?.largeText ?? ''}
+            className="w-[60px] h-[60px] rounded object-cover flex-shrink-0"
+            referrerPolicy="no-referrer"
+            loading="lazy"
+          />
+        )}
+        <div className="min-w-0 flex-1">
+          {primary.details && (
+            <div className="text-[13px] font-semibold text-txt-primary truncate">
+              {primary.details}
+            </div>
+          )}
+          {primary.state && (
+            <div className="text-[12px] text-txt-secondary truncate">{primary.state}</div>
+          )}
+          {duration > 0 ? (
+            <div className="mt-2">
+              <div className="h-[3px] rounded-full bg-interactive-muted overflow-hidden">
+                <div
+                  className="h-full bg-txt-primary rounded-full"
+                  style={{ width: `${progress * 100}%` }}
+                />
+              </div>
+              <div className="flex justify-between text-[10px] text-txt-tertiary mt-1 tabular-nums">
+                <span>{formatClock(elapsed)}</span>
+                <span>{formatClock(duration)}</span>
+              </div>
+            </div>
+          ) : start ? (
+            <div className="text-[11px] text-txt-tertiary mt-1 tabular-nums">
+              {formatClock(elapsed)} elapsed
+            </div>
+          ) : null}
+        </div>
+      </div>
+    </div>
+  );
+}