feat(esp_libc): refactored POSIX timers get/set functions

- Added sys/timex.h and clock_adjtime API

components/esp_libc/priv_include/esp_libc_timekeeping.h

@@ -0,0 +1,43 @@
+/*
+ * SPDX-FileCopyrightText: 2026 Espressif Systems (Shanghai) CO LTD
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+#pragma once
+
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * @brief Get current realtime in microseconds (adjusted boot time + time_since_boot).
+ */
+uint64_t esp_libc_timekeeping_get_realtime_us(void);
+
+/**
+ * @brief Set realtime to the given epoch in microseconds (stops any slew, sets boot time).
+ */
+void esp_libc_timekeeping_set_realtime_us(uint64_t us);
+
+/**
+ * @brief Get remaining adjtime correction in microseconds.
+ *
+ * @return Remaining slew in microseconds.
+ */
+int64_t esp_libc_timekeeping_adjtime_get_remaining_us(void);
+
+/**
+ * @brief Apply an adjtime offset (slew) in microseconds.
+ *
+ * @param offset_us         Offset to apply in microseconds (positive or negative).
+ * @param prev_remaining_us On success, set to previous remaining correction in microseconds.
+ * @return 0 on success, -1 on error (e.g. invalid offset magnitude).
+ */
+int esp_libc_timekeeping_adjtime_apply(int64_t offset_us, int64_t *prev_remaining_us);
+
+#ifdef __cplusplus
+}
+#endif