Do these two sentences have the same meaning?
When we arrived, David had already got home
When we arrived, David was already home
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It’s a matter of emphasis. The first sentence stresses David’s action in getting home, the second his state of being there.
My intuition is that the first one leaves open the possibility that David was home, but left at some point. That is:
When we arrived, David had already got[ten] home, but had left.
is ok, but
When we arrived, David was already home, but had left.
has the ring of a contradiction.
I wouldn't lean on it too heavily. In most contexts, I think they are more or less the same.
The first sentence explicitly tells us that David had been gone, and was now back. The second implies that he had gone out, but leaves open the possibility that he had never left. The emphasis there is that there was no need to get David to come home--he was already there.