fix(dashboard): deduplicate realtime log replay

tests/dashboard/live-console-model.test.ts

@@ -38,4 +38,19 @@ describe('live console state', () => {
     expect(state.entries.map(({ id }) => id)).toEqual(['3', '4']);
     expect(state.pendingEntries).toEqual([]);
   });
+
+  it('deduplicates the same log delivered by the initial snapshot and SSE replay', () => {
+    let state = createLiveConsoleState();
+    state = reduceLiveConsoleState(state, {
+      type: 'append',
+      entry: entry('initial-1', 'info', 'Database initialized'),
+    });
+    state = reduceLiveConsoleState(state, {
+      type: 'append',
+      entry: entry('realtime-1', 'info', 'Database initialized'),
+    });
+
+    expect(state.entries).toHaveLength(1);
+    expect(state.entries[0]?.id).toBe('initial-1');
+  });
 });