How can I get the current node view mode and add to block template suggestion?
You say in your comment it is not useful for you and I doubt there are many use cases for this at all, because normally as main content a node is rendered in the full view mode.

Nonetheless trying to answer: A block is built based on contexts and at the moment this is the route, which you have to add as cache metadata to the block. You can then base the decision which view mode the node uses on this route by checking _entity_view of the route definition. If the view mode is controlled by code somewhere else you need to pull this in as context as well.