Aside from including multipolygons in your search, there is another issue.
To include ways tagged landuse=forest and natural=wood in your search result, you need to create a union of both separate sets you get. This can be archieved by enclosing both lines starting with way in brackets:

(
way...;
way...;
);

This will result in over 2000 ways for Luzern, testing queries on a smaller area might be advisable.