feat(operation): send X-Boot-Reason so power-cycle is a force-resync

Distinguish a cold-boot poll (UNDEFINED wakeup cause = power-on, hard
reset, plug-cycle) from a normal timer wake. Encoded as the
X-Boot-Reason request header; server uses it to deliberately bypass
the schedule and rotate. Matches how users actually use the device:
unplug-and-replug as a manual refresh.

Tests: two new native cases asserting the header is "cold" on
UNDEFINED wakeup and "timer" on TIMER wakeup. esp_sleep mock now
exposes a settable wakeup_cause global.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

test/mocks/esp_sleep.h

@@ -4,5 +4,19 @@
 extern uint64_t g_sleep_us;
 extern bool     g_deep_sleep_started;
 
+// Mirror of the ESP-IDF wakeup-cause enum that the firmware actually checks.
+// Tests set g_wakeup_cause directly to simulate cold-boot vs timer-wake.
+typedef enum {
+    ESP_SLEEP_WAKEUP_UNDEFINED = 0,    // cold boot / power-on / hard reset
+    ESP_SLEEP_WAKEUP_EXT0      = 2,
+    ESP_SLEEP_WAKEUP_EXT1      = 3,
+    ESP_SLEEP_WAKEUP_TIMER     = 4,    // returned to userland after deep-sleep timer
+    ESP_SLEEP_WAKEUP_TOUCHPAD  = 5,
+    ESP_SLEEP_WAKEUP_ULP       = 6,
+} esp_sleep_wakeup_cause_t;
+
+extern esp_sleep_wakeup_cause_t g_wakeup_cause;
+
 inline void esp_sleep_enable_timer_wakeup(uint64_t us) { g_sleep_us = us; }
 inline void esp_deep_sleep_start() { g_deep_sleep_started = true; }
+inline esp_sleep_wakeup_cause_t esp_sleep_get_wakeup_cause() { return g_wakeup_cause; }