I had the same question.
We found the following event in the internal logs of the Search Head were the kvstore backup was run:
127.0.0.1 - admin [03/Feb/2020:17:15:44.925 -0500] "POST /services/kvstore/backup/create HTTP/1.1" 200 1747 - - - 0ms
Otherwise we have yet to determine a reliable way to identify the status of a kvstore backup job from internal/introspection logs.
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