How can I save the original filename to the database?

How about saving the original filename inside the current $_REQUEST and processing it whenever WordPress generates the attachment metadata:

/**
 * Store original attachment filename in the current $_REQUEST superglobal
 * 
 * @param NULL
 * @param Array $file - Uploaded File Information
 * 
 * @return NULL
 */
function wpse342438_store_attachment_filename( $null, $file ) {

    $_REQUEST['original_filename'] = basename( $file['name'] );

    return $null;

}
add_filter( 'pre_move_uploaded_file', 'wpse342438_store_attachment_filename', 10, 2 );

/**
 * Save original filename if it exists in our $_REQUEST
 * 
 * @param Array $metadata           - Generated Attachment Metadata
 * @param Integer $attachment_id    - WordPress Attachment Post ID
 * 
 * @return Array $metadata
 */
function wpse342438_save_original_filename( $metadata, $attachment_id ) {

    if( ! empty( $_REQUEST['original_filename'] ) ) {
        update_post_meta( $attachment_id, '_original_filename', sanitize_text_field( $_REQUEST['original_filename'] ) );
    }

    return $metadata;

}
add_filter( 'wp_generate_attachment_metadata', 'wpse342438_save_original_filename', 10, 2 );

The pre_move_uploaded_file hook should fire before your uploaded file moves from the tmp directory to the actual WordPress uploads folder structure. The wp_generate_attachment_metadata hook should run every time an attached is added to the database so it can created related postmeta. If the original_filename key exists in the request by the time we get here, we can set it.

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