[core] optimize #include directives in core cpp files (#10717)

This commit removes unnecessary `#include` directives in core `cpp`
files that already include `instance.hpp`. The `instance.hpp` header
itself includes all necessary OT core headers and definitions as they
are contained within an `ot::Instance`.

src/core/common/notifier.cpp

@@ -33,11 +33,6 @@
 
 #include "notifier.hpp"
 
-#include "border_router/routing_manager.hpp"
-#include "common/array.hpp"
-#include "common/code_utils.hpp"
-#include "common/debug.hpp"
-#include "common/log.hpp"
 #include "instance/instance.hpp"
 
 namespace ot {