[Cleanup] Add missing #include. Remove useless ones. IWYU part 2.

This is a follow-up to
https://webrtc-review.googlesource.com/c/src/+/106280.
This time the whole code base is covered.
Some files may have not been fixed though, whenever the IWYU tool
was breaking the build.

Bug: webrtc:8311
Change-Id: I2c31f552a87e887d33931d46e87b6208b1e483ef
Reviewed-on: https://webrtc-review.googlesource.com/c/111965
Commit-Queue: Yves Gerey <yvesg@google.com>
Reviewed-by: Karl Wiberg <kwiberg@webrtc.org>
Reviewed-by: Mirko Bonadei <mbonadei@webrtc.org>
Cr-Commit-Position: refs/heads/master@{#25830}

modules/BUILD.gn

@@ -236,6 +236,7 @@ if (rtc_include_tests) {
 
     deps = [
       ":module_api",
+      ":module_api_public",
       "../test:test_main",
       "../test:test_support",
       "audio_coding:audio_coding_unittests",