First, the ideal way to handle cover artwork is for it to be embedded within your audio files in the first place so Poweramp doesn't need to download it separately. That way the correct image is always part of the song file, and will remain with it wherever you use that audio file. This is something you need to do outside of Poweramp though, using tag editing software.
However if embedded artwork is not found, Poweramp can automatically search online for matching images. This feature can be enabled and configured via the options in PA Settings > Album Art. If you don't happen to like a picture it finds you can manually select your own image by long-pressing on the song title (or on the album cover area in the player screen) and choosing 'Album Art'.
For older versions of Android (prior to Android 10/11) Poweramp uses a custom location on internal device storage for saving these image files: Android/data/_com.maxmpz.audioplayer/ (note the underscore in '_com'). If PA was first installed that way, that folder will most likely still remain in use currently - even if you have updated your Android ROM and/or Poweramp version.
For newer versions of Android (11+) and recent builds of Poweramp, changes in the Android system requirements mean newly installed apps have to use a single specific internal storage folder for data, which in Poweramp's case means cover artwork can now be found in: Android/data/com.maxmpz.audioplayer/files/ (no underscore).
Whichever of these two base locations is being used on your device, you will find several subfolders for various different types of saved artwork. The 'selected_' folder names are used for images that you manually chose, which will override any automated downloads:
album_art or selected_aa for album covers as used in album/song lists, and on the player screen.
artist_art or selected_artist for artist images used in the Artists category.
composer_art or selected_composer for composer images used in the Composers category.
genre_art or selected_genre for genre images used in Genres category.
playlist_art or selected_playlist for playlists as shown in the Playlists category.
The actual filename used for each entry will match with the tagged information held in PA's song database - such as <artistname>.jpg, <aristname> - <albumtitle>.jpg, or <playlistname>.jpg - with most special characters (*, $, %, &, ;, brackets, etc) replaced with underscores. The easiest way to see how it works is to look at existing items in these folders.
You can edit or create these JPG files if you wish, but make sure the naming convention remains precisely as Poweramp defined it. Changes will get included as you navigate through lists, or to force a complete refresh you can fully exit and restart the Poweramp app.
Please also see the general FAQ on how cover artwork is chosen for display, which includes other ways that you can provide images: