You can use the post_password_required
filter.
function wpse406803_whitelist_author( $required, $post ) {
//Check if current user is the post author
if ( $post->post_author == get_current_user_id() ) {
return false;
}
}
add_filter( 'post_password_required', 'wpse406803_whitelist_author', 10, 2 );