Why aren't my local tasks shown?
Since everything looked just fine in your code, I tried the following in a custom module: 

#test.links.task.yml
test.node_test:
   title: 'Wooorking'
   route_name: entity.node.canonical
   base_route: entity.node.canonical


And this is working like a charm. Also when I added a custom routing, which was pointing to a form controller, it showed up! (although not worked, because I didn't handled the node parameter in the routing configuration)

So the problem lies another where. 

So I suggest you to do it step by step way (building your routing and task yml) to understand your problem. Clearing the cache each time when you change something in your YML files. If you found the problem, please post the solution, so also we can learn from this.