Stage 8 polish: iPhone refinements (keyboard, native pickers, compact invite)

Second owner-review pass (iPhone simulator):
- Chat (and the modal) are sized in dvh so they shrink above the software keyboard,
  keeping the start of the conversation on screen instead of pushed off the top.
- The profile away window returns to a native <input type="time" step="600"> (the iOS
  wheel with 10-minute steps) instead of separate dropdowns; the timezone stays a
  native offset <select>.
- A finished game reserves the rack's height (min-height) so the footer no longer
  collapses when the final rack is empty — no layout jump versus an active game.
- New-game "play with friends" is made compact: a searchable, bounded-scroll friend
  list, the game-type / move-time / hints controls as native selects in one row
  (labels above), and Send invitation pinned at the bottom — it scales to many friends.

ui/src/components/Modal.svelte

@@ -36,7 +36,10 @@
     box-shadow: var(--shadow);
     padding: var(--pad);
     width: min(94vw, 420px);
+    /* dvh tracks the dynamic viewport, so the sheet shrinks above an open mobile
+       keyboard instead of being scrolled off the top (vh fallback first). */
     max-height: 86vh;
+    max-height: 86dvh;
     overflow: auto;
   }
   h2 {