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You are using a <section> for your map and not a <div>.
That might not be 100% true but it has something to do all the sections in the map domNode.
Scratch previous. The logo is there but map overflow is hidden. Why put all those extra elements in the map's domNode? They are making the map overflow. The only thing you should have in the map in the home button div.
I see. You can use a border container as a region (no height or width required). Set the toolbar as the top region and the map as the center region therein.