Scope dial polish (Codex): hero stays closest-first + visible Clear

- Hero constraint: _pick_lead now runs only within the CLOSEST non-empty section of a
  personalized Brief, so a "gentler" wider-region/world story can never be floated into
  the hero slot above a local one. Only widens if the closest section is empty.
- Dial gains a visible Clear (alongside Change) so a reader never feels locked into
  personalization; "World" stays the keep-home-but-go-global option.

366 tests green.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/src/routes/+page.svelte

@@ -738,7 +738,10 @@
                   <button class="sd-btn" class:on={homeScope === s} onclick={() => setScope(s)}>{label}</button>
                 {/each}
               </div>
-              <button class="linkish sd-change" onclick={openHomeEditor}>Change home</button>
+              <span class="sd-actions">
+                <button class="linkish" onclick={openHomeEditor}>Change</button>
+                <button class="linkish" onclick={clearHome}>Clear</button>
+              </span>
             </div>
           {/if}
           <section class="rise">
@@ -1047,7 +1050,7 @@
             background: var(--bg); color: var(--ink); cursor: pointer; border-right: 1px solid var(--line); }
   .sd-stops .sd-btn:last-child { border-right: none; }
   .sd-btn.on { background: var(--accent-soft); color: var(--accent-deep); }
-  .sd-change { margin-left: auto; }
+  .sd-actions { margin-left: auto; display: inline-flex; gap: 12px; }
   .feed-section { grid-column: 1 / -1; margin: 8px 0 2px; font-family: var(--label); font-size: 0.78rem;
                   text-transform: uppercase; letter-spacing: 0.06em; color: var(--muted); }
   .grid > .feed-section:first-child { margin-top: 0; }