I’m getting Call to undefined function wp_parse_list() out of the blue

it looks like this is a new function since 5.1.0. see that info here: https://de.wpseek.com/function/wp_parse_list/

you could try to add this in your themes function.php temporarily, as a workaround.

function wp_parse_list( $list ) {
    if ( ! is_array( $list ) ) {
        return preg_split( '/[\s,]+/', $list, -1, PREG_SPLIT_NO_EMPTY );
    }

    return $list;
}

so as you guess: i think it’s something related with caching, too.