Block in node view showing but does not show up when rendering node in Views
You are mixing up full node (view mode) and single node (page, canonical URL). Blocks only get added to pages. In regions.
I'm not sure right now, but isn't there from core already a block reference field you can add to a node type? Use this. Or use the Block Field module. And then set your specific block as default value.
Alternatively you can use a pseudo field (a.k.a extra field) from a custom module to render your block. Has the advantage that it then can't be changed by editors.