[ResponseOps][Cases] Add timing metrics to cases SO (elastic#219070)

## Summary

- Adds the `in_progress_at` timestamp to Cases Saved Objects
- Adds the `time_to_acknowledge`, `time_to_investigate` and
`time_to_resolve` timing metrics to Cases Saved Objects

## References

Closes elastic#217638

### Checklist

Check the PR satisfies following conditions. 

Reviewers should verify this PR satisfies this list as well.

- [x] [Unit or functional
tests](https://www.elastic.co/guide/en/kibana/master/development-tests.html)
were updated or added to match the most common scenarios
- [x] [Flaky Test
Runner](https://ci-stats.kibana.dev/trigger_flaky_test_runner/1) was
used on any tests changed (passed ✅)

---------

Co-authored-by: kibanamachine <42973632+kibanamachine@users.noreply.github.com>
Co-authored-by: Christos Nasikas <xristosnasikas@gmail.com>
Co-authored-by: Christos Nasikas <christos.nasikas@elastic.co>

Author: 3 people

x-pack/platform/plugins/shared/cases/common/types/domain/case/v1.test.ts

@@ -93,6 +93,10 @@ const basicCase = {
   ],
   observables: [],
   incremental_id: undefined,
+  in_progress_at: undefined,
+  time_to_acknowledge: undefined,
+  time_to_investigate: undefined,
+  time_to_resolve: undefined,
 };
 
 describe('RelatedCaseRt', () => {
@@ -207,7 +211,10 @@ describe('CaseAttributesRt', () => {
       },
     ],
     observables: [],
-    incremental_id: undefined,
+    in_progress_at: undefined,
+    time_to_acknowledge: undefined,
+    time_to_investigate: undefined,
+    time_to_resolve: undefined,
   };
 
   it('has expected attributes in request', () => {

x-pack/platform/plugins/shared/cases/common/types/domain/case/v1.ts

@@ -130,6 +130,10 @@ export const CaseAttributesRt = rt.intersection([
   rt.exact(
     rt.partial({
       incremental_id: rt.union([rt.number, rt.null]),
+      in_progress_at: rt.union([rt.string, rt.null]),
+      time_to_acknowledge: rt.union([rt.number, rt.null]),
+      time_to_investigate: rt.union([rt.number, rt.null]),
+      time_to_resolve: rt.union([rt.number, rt.null]),
     })
   ),
 ]);

x-pack/platform/plugins/shared/cases/server/client/cases/bulk_update.test.ts

@@ -32,6 +32,7 @@ describe('update', () => {
       },
     ],
   };
+
   const casesClientMock = createCasesClientMock();
   casesClientMock.configure.get = jest.fn().mockResolvedValue([]);
 
@@ -1896,4 +1897,48 @@ describe('update', () => {
       });
     });
   });
+
+  describe('Metrics', () => {
+    const clientArgs = createCasesClientMockArgs();
+
+    beforeEach(() => {
+      jest.clearAllMocks();
+      clientArgs.services.caseService.getCases.mockResolvedValue({ saved_objects: mockCases });
+      clientArgs.services.caseService.getAllCaseComments.mockResolvedValue({
+        saved_objects: [],
+        total: 0,
+        per_page: 10,
+        page: 1,
+      });
+
+      clientArgs.services.caseService.patchCases.mockResolvedValue({
+        saved_objects: mockCases,
+      });
+
+      clientArgs.services.attachmentService.getter.getCaseCommentStats.mockResolvedValue(new Map());
+    });
+
+    it('calculates metrics correctly', async () => {
+      await bulkUpdate(
+        {
+          cases: [
+            {
+              id: mockCases[0].id,
+              version: mockCases[0].version ?? '',
+              status: CaseStatuses.closed,
+            },
+          ],
+        },
+        clientArgs,
+        casesClientMock
+      );
+
+      const updatedAttributes =
+        clientArgs.services.caseService.patchCases.mock.calls[0][0].cases[0].updatedAttributes;
+
+      expect(updatedAttributes.time_to_acknowledge).toEqual(expect.any(Number));
+      expect(updatedAttributes.time_to_investigate).toEqual(expect.any(Number));
+      expect(updatedAttributes.time_to_resolve).toEqual(expect.any(Number));
+    });
+  });
 });

x-pack/platform/plugins/shared/cases/server/client/cases/bulk_update.ts

@@ -44,6 +44,8 @@ import {
   fillMissingCustomFields,
   getClosedInfoForUpdate,
   getDurationForUpdate,
+  getInProgressInfoForUpdate,
+  getTimingMetricsForUpdate,
 } from './utils';
 import { LICENSING_CASE_ASSIGNMENT_FEATURE } from '../../common/constants';
 import type { LicensingService } from '../../services/licensing';
@@ -656,6 +658,17 @@ const createPatchCasesPayload = ({
             closedAt: updatedDt,
             createdAt: originalCase.attributes.created_at,
           }),
+          ...getInProgressInfoForUpdate({
+            status: trimmedCaseAttributes.status,
+            stateTransitionTimestamp: updatedDt,
+            inProgressAt: originalCase.attributes.in_progress_at,
+          }),
+          ...getTimingMetricsForUpdate({
+            status: trimmedCaseAttributes.status,
+            stateTransitionTimestamp: updatedDt,
+            createdAt: originalCase.attributes.created_at,
+            inProgressAt: originalCase.attributes.in_progress_at,
+          }),
           updated_at: updatedDt,
           updated_by: user,
         },

x-pack/platform/plugins/shared/cases/server/client/cases/push.ts

@@ -31,7 +31,12 @@ import {
   OWNER_FIELD,
 } from '../../../common/constants';
 
-import { createIncident, getDurationInSeconds, getUserProfiles } from './utils';
+import {
+  createIncident,
+  getDurationInSeconds,
+  getTimingMetricsForUpdate,
+  getUserProfiles,
+} from './utils';
 import { createCaseError } from '../../common/error';
 import {
   createAlertUpdateStatusRequest,
@@ -230,6 +235,14 @@ export const push = async (
                 createdAt: theCase.created_at,
               })
             : {}),
+          ...(shouldMarkAsClosed
+            ? getTimingMetricsForUpdate({
+                status: CaseStatuses.closed,
+                stateTransitionTimestamp: pushedDate,
+                createdAt: theCase.created_at,
+                inProgressAt: theCase.in_progress_at,
+              })
+            : {}),
           external_service: externalService,
           updated_at: pushedDate,
           updated_by: { username, full_name, email, profile_uid },