esp_hw_support/esp_system: Re-evaluate header inclusions and include directories

This commit updates the visibility of various header files and cleans up
some unnecessary inclusions. Also, this commit removes certain header
include paths which were maintained for backward compatibility.

components/newlib/random.c

@@ -1,23 +1,15 @@
-// Copyright 2018 Espressif Systems (Shanghai) PTE LTD
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+/*
+ * SPDX-FileCopyrightText: 2018-2022 Espressif Systems (Shanghai) CO LTD
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ */
 
 #include <sys/random.h>
 #include <sys/param.h>
 #include <assert.h>
 #include <errno.h>
 #include <string.h>
-#include "esp_system.h"
+#include "esp_random.h"
 #include "esp_log.h"
 
 static const char *TAG = "RANDOM";