Please try to understand this question carefully before marking this as duplicate. Do the Android OS has inbuilt support for .zip and .rar files ? I am not asking about any third-party software, because I know that there is a difference between OS support and software support. I am asking this because I have found bootanimation.zip and shutdownanimation.zip files inside /system/media/ folder.
Android does not contain any program-code for reading or writing RAR files.
For ZIP files Android has support for reading/extracting and creating new ZIP files (Android APK app files are ZIP files therefore reading them is required for running Android).
However the functions for handling ZIP files are only available on development level, therefore any Android app can read or create ZIP files.
The only app I know that can handle ZIP files is the default app Files (com.android.documentsui) which is available by default on a large number of devices (some vendors replace this app therefore it is not available on each an every device). Note that this app is not available in the Google PlayStore.
There are no command-line programs that can handle ZIP files (to be used e.g. via adb)