Surface stop_timeout on the Instance response

stop_timeout was settable at create but not returned on the Instance
object, so clients couldn't read back what they configured. Add it to
the Instance schema and map it in instanceToOAPI, emitting the
configured value when set and omitting it when unset (server default
applies) — symmetric with the request-side semantics.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

Author: Sayan-

cmd/api/api/instances.go

@@ -1183,6 +1183,10 @@ func instanceToOAPI(inst instances.Instance) oapi.Instance {
 		oapiInst.ExitMessage = lo.ToPtr(inst.ExitMessage)
 	}
 
+	if inst.StopTimeout > 0 {
+		oapiInst.StopTimeout = lo.ToPtr(inst.StopTimeout)
+	}
+
 	if len(inst.Env) > 0 {
 		oapiInst.Env = &inst.Env
 	}

cmd/api/api/instances_test.go

@@ -635,6 +635,44 @@ func TestInstanceToOAPI_OmitsPlatformWhenUnset(t *testing.T) {
 	assert.Nil(t, oapiInst.Platform)
 }
 
+func TestInstanceToOAPI_EchoesStopTimeout(t *testing.T) {
+	t.Parallel()
+
+	inst := instances.Instance{
+		StoredMetadata: instances.StoredMetadata{
+			Id:             "inst-stop-timeout",
+			Name:           "inst-stop-timeout",
+			Image:          "docker.io/library/alpine:latest",
+			CreatedAt:      time.Now(),
+			HypervisorType: hypervisor.TypeCloudHypervisor,
+			StopTimeout:    30,
+		},
+		State: instances.StateRunning,
+	}
+
+	oapiInst := instanceToOAPI(inst)
+	require.NotNil(t, oapiInst.StopTimeout)
+	assert.Equal(t, 30, *oapiInst.StopTimeout)
+}
+
+func TestInstanceToOAPI_OmitsStopTimeoutWhenUnset(t *testing.T) {
+	t.Parallel()
+
+	inst := instances.Instance{
+		StoredMetadata: instances.StoredMetadata{
+			Id:             "inst-no-stop-timeout",
+			Name:           "inst-no-stop-timeout",
+			Image:          "docker.io/library/alpine:latest",
+			CreatedAt:      time.Now(),
+			HypervisorType: hypervisor.TypeCloudHypervisor,
+		},
+		State: instances.StateStopped,
+	}
+
+	oapiInst := instanceToOAPI(inst)
+	assert.Nil(t, oapiInst.StopTimeout)
+}
+
 // errCreateInstanceManager is a fake whose CreateInstance always fails with a
 // preset error, used to assert the handler maps typed image errors to statuses.
 type errCreateInstanceManager struct {