Home/Calendar polish: person switcher placement, full-width Calendar, sponsors

- Home: the person switcher (chip row) now lives in the white content area
  instead of the navy header, matching the design canvas's own M1 markup,
  and renders smaller. Home is now the only screen that shows it at all.
- Calendar: dropped the person switcher and the "My schedule"/"All members"
  toggle entirely -- it always shows every event self.managed_people is
  invited to, full stop. Rows now run edge-to-edge (-mx-4) instead of
  living in a rounded, inset card, matching the M3 design canvas's own
  full-bleed layout. (The design mock's List/Month/"Games only" controls
  aren't reproduced -- no real functionality behind them yet.)
- Home's "Needs your answer" card caps at 5 items with a "+N more in
  Calendar" link, so it can't crowd the dues/news cards below it off the
  first screenful.
- Home gains a sponsors strip at the very bottom (horizontally scrolling,
  scrollbar hidden) -- active sponsors only, reshuffled on every request.
  club.services.sponsors.active_sponsors factors the "what counts as
  active" query out of club/api.py's public sponsors endpoint so both it
  and Home share one definition.
- Also removed mobile/views.py's now-fully-dead _PlaceholderScreen and its
  template -- every M1-M7 screen has had a real implementation for a while
  and nothing subclassed it anymore.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01ECGMEwrc2k4D8VQuwjstj9

assets/mobile.css

@@ -380,16 +380,16 @@
         border: 1px solid #dde1e7;
     }
 
-    /* --- Person switcher chips (M1, M2, M3 -- "a person switcher on anything per-member") --- */
+    /* --- Person switcher chips (Home's own -- see mobile/templates/mobile/home.html) --- */
 
     .person-chip {
         display: flex;
         align-items: center;
-        gap: 8px;
+        gap: 6px;
         background: #fff;
         border: 1.5px solid var(--color-line);
         border-radius: 999px;
-        padding: 5px 12px 5px 5px;
+        padding: 4px 10px 4px 4px;
         color: var(--color-muted);
         flex-shrink: 0;
     }
@@ -400,8 +400,8 @@
     }
 
     .person-chip-avatar {
-        width: 28px;
-        height: 28px;
+        width: 22px;
+        height: 22px;
         border-radius: 999px;
         background: var(--color-stroke);
         color: #fff;
@@ -410,7 +410,7 @@
         justify-content: center;
         font-family: var(--font-display);
         font-weight: 800;
-        font-size: 0.875rem;
+        font-size: 0.6875rem;
         flex-shrink: 0;
     }
 
@@ -421,7 +421,7 @@
     .person-chip-label {
         font-family: var(--font-display);
         font-weight: 700;
-        font-size: 0.9375rem;
+        font-size: 0.8125rem;
         letter-spacing: 0.06em;
         text-transform: uppercase;
     }