feat: rename delaymgr precision→precision_ms, replace sleep() with nanosleep() (P0-2b)

- Rename `precision` field to `precision_ms` in delaymgr_t struct (delay.h)
- Replace `sleep(mgr->precision)` with `nanosleep()` for 10ms granularity (delay.c)
- Add `#include <time.h>` to delay.c (already in delay.h)
- Update delaymgr_init() to store precision_ms parameter
- Update all call sites: cluster.c (2→200ms), controller/testsuite/test.c (2→2000ms),
  lib/testsuite/test_delay.c (1→1000ms)
- Add TDD test test_delaymgr_precision_ms_field verifying field exists and stores correctly
- delay_task() delay parameter remains in seconds; only sleep granularity changes

src/lib/delay.c

@@ -3,6 +3,7 @@
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
+#include <time.h>
 
 #include "delay.h"
 #include "utils.h"
@@ -17,7 +18,10 @@ static void* delay_worker(void* args)
         time_t        now;
 
         pthread_testcancel();
-        sleep(mgr->precision);
+        {
+            struct timespec ts = { 0, (long)mgr->precision_ms * 1000000L };
+            nanosleep(&ts, NULL);
+        }
 
         it = ordq_peek(&(mgr->tasks), NULL);
         if (it == NULL) {
@@ -100,7 +104,7 @@ int delaymgr_init(delaymgr_t* mgr, int precision, task_run_fn_t runner_fn)
         runner_fn = default_runner_fn;
     }
 
-    mgr->precision = precision;
+    mgr->precision_ms = precision;
     mgr->running   = 0;
     mgr->runner_fn = runner_fn;
     mgr->worker    = 0;

src/lib/testsuite/test_delay.c

@@ -26,7 +26,7 @@ static void test_delay1()
     int        delay_period = 2;
     time_t     t_start      = time(NULL);
 
-    delaymgr_init(&mgr, 1, NULL);
+    delaymgr_init(&mgr, 1000 /* precision_ms */, NULL);
     delaymgr_start(&mgr);
     delay_task(&mgr, delay_period, runcount, (delay_task_entry_fn_t)delay_work,
                &count);
@@ -48,9 +48,22 @@ static void test_delay1()
     return;
 }
 
+static void test_delaymgr_precision_ms_field(void)
+{
+    delaymgr_t mgr;
+    memset(&mgr, 0, sizeof(mgr));
+    /* precision_ms field must exist and be stored correctly */
+    int rc = delaymgr_init(&mgr, 200 /* precision_ms */, NULL);
+    TEST_ASSERT_EQUAL_INT(0, rc);
+    TEST_ASSERT_EQUAL_INT(200, mgr.precision_ms);
+    delaymgr_fini(&mgr);
+    printf("test_delaymgr_precision_ms_field: PASS\n");
+}
+
 void test_delay(void)
 {
     printf("\n>> delay test\n\n");
 
     RUN_TEST(test_delay1);
+    RUN_TEST(test_delaymgr_precision_ms_field);
 }