+// probeAndUpdate calls probeBooted and/or probeRunning if needed, and
+// updates state accordingly.
+//
+// In StateUnknown: Call both probeBooted and probeRunning.
+// In StateBooting: Call probeBooted; if successful, call probeRunning.
+// In StateRunning: Call probeRunning.
+// In StateIdle: Call probeRunning.
+// In StateShutdown: Do nothing.
+//
+// If both probes succeed, wkr.state changes to
+// StateIdle/StateRunning.
+//
+// If probeRunning succeeds, wkr.running is updated. (This means
+// wkr.running might be non-empty even in StateUnknown, if the boot
+// probe failed.)
+//
+// probeAndUpdate should be called in a new goroutine.