Downloaded files are stored in external private storage (Android/data/com.github.libretube).
Note that since Android 11, the READ_EXTERNAL_STORAGE permission does not grant third party apps access to external private storage, requiring workarounds.
The (usually hidden, not to be confused with Files by Google) Android built-in Files app will always have access to this directory.
In the downloaded files, audio and video are separated. Hence it is recommended to exclusively use LibreTube for playing downloaded media.