Probe hosts for health instead of risking the shared connection

The health check shares each host's libvirt connection with the reconciles,
so it must not be able to take that connection away from them.

- A timed-out check no longer drops the link. The check goes through the new
  hostPool.probe, which abandons its RPCs when the context ends and leaves
  the connection alone, so an image upload or a Create running on the same
  link is not cut off. A link that really died is closed by the keepalive.
  One abandoned probe per host may stay waiting; until it returns, the next
  check reports Timeout at once (errProbeBusy).
- Waiting for a host's connection slot now ends with the caller's context.
  hostEntry used a mutex, so a check could wait out a reconcile redialing a
  dead host — minutes — past its own timeout. The slot is a one-slot channel
  and acquire bounds only the wait, never the uncontended take.
- --provider-check-timeout defaults to 0 and derives min(15s, interval).
  The flat 15s default contradicted the validation that the timeout may not
  exceed the interval, so --provider-check-interval=12s alone failed to
  start.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

internal/providerhealth/monitor_test.go

@@ -340,7 +340,8 @@ func TestValidateSchedule(t *testing.T) {
 		{"shortest interval", 10 * time.Second, 10 * time.Second, false},
 		{"too frequent", 5 * time.Second, time.Second, true},
 		{"negative interval", -time.Minute, time.Second, true},
-		{"no timeout", time.Minute, 0, true},
+		{"timeout left to derive, short interval", 12 * time.Second, 0, false},
+		{"negative timeout", time.Minute, -time.Second, true},
 		{"timeout longer than interval", time.Minute, 2 * time.Minute, true},
 	}
 	for _, tc := range tests {
@@ -352,3 +353,25 @@ func TestValidateSchedule(t *testing.T) {
 		})
 	}
 }
+
+func TestMonitor_setDefaults_timeout(t *testing.T) {
+	t.Parallel()
+	tests := []struct {
+		name                    string
+		interval, timeout, want time.Duration
+	}{
+		{"default", time.Minute, 0, 15 * time.Second},
+		{"interval shorter than the default", 12 * time.Second, 0, 12 * time.Second},
+		{"explicit", time.Minute, 20 * time.Second, 20 * time.Second},
+	}
+	for _, tc := range tests {
+		t.Run(tc.name, func(t *testing.T) {
+			t.Parallel()
+			m := &Monitor{Interval: tc.interval, Timeout: tc.timeout}
+			m.setDefaults()
+			if m.Timeout != tc.want {
+				t.Errorf("Timeout = %s, want %s", m.Timeout, tc.want)
+			}
+		})
+	}
+}