feat(ui): the search palette, entry points and a trail that survives the URL (CG-45)

Search: `/` or ⌘K focuses the box; results arrive grouped by kind with their
glyph, signature and file:line, ↑/↓/Enter walk them, Esc dismisses. A group
appears where its best result did, so flattening the groups reproduces the
ranking the keyboard walks — the panel's flat item list IS that concatenation.
A flow question ("how does X reach Y", "X -> Y") is recognised and searches
both endpoints with a note, rather than offering a row that would land on the
phase-2 Flow view.

Entry points answer "where do I start" on the empty screen and in the resting
palette, all derived from the graph: routes, files that run something at module
level (the engine records a top-level statement as an edge out of the file node,
which is what makes src/bin/codegraph.ts the root of the CLI flow — ranked by
calls x the files they reach, so a registration table calling into itself does
not outrank the CLI), and the most depended-on symbols. Tests are excluded from
both derived lists.

Trail: hops record the direction they were walked (→ into a call, ← up to a
caller), clicking one truncates back to it, Clear keeps the place instead of
throwing it away, and the whole walk travels in the URL. A shared or reloaded
trail arrives as ids, so hops learn their names back through a new batch
endpoint and a session name cache — without it, walking back across a
truncation redrew earlier hops as raw hashes. "Read as flow" stays hidden until
there is a Flow view to send it to.

New endpoints: /api/entrypoints and /api/nodes. New engine reads:
getTopCallingFiles, getFileDependentCounts.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

ui/src/views/HomeView.svelte

@@ -1,8 +1,40 @@
 <script lang="ts">
+  /**
+   * The empty screen — and the answer to "where do I start".
+   *
+   * Nothing selected is the normal first state of a viewer opened on a project
+   * nobody has read before, so it carries the same entry points the palette
+   * shows at rest, at full length: the routes a request arrives on, the files
+   * that run something at module level, and the symbols the most code depends
+   * on. Every one of them is derived from the graph — see
+   * `src/ui-server/api/entrypoints.ts` for what each is derived from.
+   */
+  import PaletteRows from '../components/PaletteRows.svelte';
+  import { palette } from '../lib/palette.svelte';
+  import { buildEntryPalette, type PaletteItem } from '../lib/search-model';
+  import { walkTo } from '../lib/walk';
+
   interface Props {
     project?: string | null;
   }
   let { project = null }: Props = $props();
+
+  $effect(() => {
+    void palette.ensureEntries();
+  });
+
+  let entries = $derived(buildEntryPalette(palette.entries));
+
+  function pick(item: PaletteItem) {
+    const id = item.type === 'route' ? item.nodeId : item.id;
+    if (!id) return;
+    walkTo(
+      item.type === 'route'
+        ? { id, name: item.handler, kind: null }
+        : { id, name: item.node.name, kind: item.node.kind },
+      'start'
+    );
+  }
 </script>
 
 <div class="scroll">
@@ -17,6 +49,15 @@
       what it calls on the right — each callee lined up with the line that makes the call.
     </p>
   </div>
+
+  {#if entries.sections.length > 0}
+    <section class="entries" aria-label="Where to start">
+      <h3>Where to start</h3>
+      <div class="rows">
+        <PaletteRows palette={entries} onpick={pick} />
+      </div>
+    </section>
+  {/if}
 </div>
 
 <style>
@@ -24,4 +65,25 @@
     height: 100%;
     overflow: auto;
   }
+
+  /* `.emptystate` itself is global (app.css) and shared with the other views;
+     only its bottom padding changes here, to sit against the list below. */
+  .scroll :global(.emptystate) {
+    padding-bottom: 8px;
+  }
+
+  .entries {
+    max-width: 720px;
+    padding: 8px 40px 48px;
+  }
+
+  .entries h3 {
+    margin: 0 0 8px;
+    font-size: 14px;
+    font-weight: 600;
+  }
+
+  .rows {
+    border: 1px solid var(--rule-soft);
+  }
 </style>