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Putin interprets everything that the "West" does in relation to Ukraine as saber-rattling so I don't think that giving an advance warning of the visit makes much difference in his mind.

Of course, this visit from Biden sends a message to the Kremlin but your view that the advance warning is somehow a show of cowardice is one that is colored by your dislike of the current president of the US (in my opinion).

The decision to inform an adversarial entity of the visit from the US head of state in an active war zone was likely taken by the security apparatus of Joe Biden (those types of decisions usually are).

In my view, having the Kremlin know that the president of the country with the second-largest nuclear arsenal will be present in Kyiv is probably a good idea in order to not trigger a direct act of war between both countries.