feat(documents): add GET /api/documents/density endpoint (#385)

Authenticated read endpoint backing the timeline density widget. Optional
from/to LocalDate query params narrow the aggregation. Response carries
Cache-Control: private, max-age=300 so repeated browse sessions skip the
aggregation query (per Tobias' devops review). No @RequirePermission needed —
inherits the global anyRequest().authenticated() rule.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/src/test/java/org/raddatz/familienarchiv/document/DocumentControllerTest.java

@@ -1240,4 +1240,60 @@ class DocumentControllerTest {
                 .andExpect(jsonPath("$.errors[0].message").value(
                         org.hamcrest.Matchers.containsString("not found")));
     }
+
+    // ─── GET /api/documents/density ───────────────────────────────────────────
+
+    @Test
+    void density_returns401_whenUnauthenticated() throws Exception {
+        mockMvc.perform(get("/api/documents/density"))
+                .andExpect(status().isUnauthorized());
+    }
+
+    @Test
+    @WithMockUser
+    void density_returns200_withResultBody_whenAuthenticated() throws Exception {
+        when(documentService.getDensity(any(), any())).thenReturn(
+                new DocumentDensityResult(
+                        List.of(new MonthBucket("1915-08", 2), new MonthBucket("1915-09", 1)),
+                        java.time.LocalDate.of(1915, 8, 3),
+                        java.time.LocalDate.of(1915, 9, 1)));
+
+        mockMvc.perform(get("/api/documents/density"))
+                .andExpect(status().isOk())
+                .andExpect(jsonPath("$.buckets").isArray())
+                .andExpect(jsonPath("$.buckets[0].month").value("1915-08"))
+                .andExpect(jsonPath("$.buckets[0].count").value(2))
+                .andExpect(jsonPath("$.minDate").value("1915-08-03"))
+                .andExpect(jsonPath("$.maxDate").value("1915-09-01"));
+    }
+
+    @Test
+    @WithMockUser
+    void density_emitsPrivateCacheControlHeader() throws Exception {
+        when(documentService.getDensity(any(), any())).thenReturn(
+                new DocumentDensityResult(List.of(), null, null));
+
+        mockMvc.perform(get("/api/documents/density"))
+                .andExpect(status().isOk())
+                .andExpect(header().string("Cache-Control",
+                        org.hamcrest.Matchers.containsString("max-age=300")))
+                .andExpect(header().string("Cache-Control",
+                        org.hamcrest.Matchers.containsString("private")));
+    }
+
+    @Test
+    @WithMockUser
+    void density_passesFromAndToParametersToService() throws Exception {
+        when(documentService.getDensity(any(), any())).thenReturn(
+                new DocumentDensityResult(List.of(), null, null));
+
+        mockMvc.perform(get("/api/documents/density")
+                        .param("from", "1914-01-01")
+                        .param("to", "1918-12-31"))
+                .andExpect(status().isOk());
+
+        verify(documentService).getDensity(
+                java.time.LocalDate.of(1914, 1, 1),
+                java.time.LocalDate.of(1918, 12, 31));
+    }
 }