searchsource persistable state service implementation

[ppisljar]

Summary

resolves #106517

Checklist

Delete any items that are not applicable to this PR.

• Unit or functional tests were updated or added to match the most common scenarios

[elasticmachine]

Pinging @elastic/kibana-app-services (Team:AppServices)

[kibanamachine]

💔 Build Failed

• continuous-integration/kibana-ci/pull-request
• Commit: 3a58ec9
• Storybooks Preview
• Pipeline Steps (look for red circles / failed steps)
• Interpreting CI Failures

Failed CI Steps

• Jest Unit Tests
• Check Doc API Changes

---

Test Failures

Kibana Pipeline / jest / Jest Tests.src/plugins/data/common/search/search_source.SearchSource service start() exposes proper contract

Link to Jenkins

Standard Out

Failed Tests Reporter:
  - Test has not failed recently on tracked branches

Stack Trace

Error: expect(received).toEqual(expected) // deep equality

- Expected  - 0
+ Received  + 4

  Array [
    "create",
    "createEmpty",
+   "extract",
+   "inject",
+   "getAllMigrations",
+   "migrateToLatest",
  ]
    at Object.<anonymous> (/var/lib/jenkins/workspace/elastic+kibana+pipeline-pull-request/kibana/src/plugins/data/common/search/search_source/search_source_service.test.ts:31:34)
    at Object.asyncJestTest (/var/lib/jenkins/workspace/elastic+kibana+pipeline-pull-request/kibana/node_modules/jest-jasmine2/build/jasmineAsyncInstall.js:106:37)
    at /var/lib/jenkins/workspace/elastic+kibana+pipeline-pull-request/kibana/node_modules/jest-jasmine2/build/queueRunner.js:45:12
    at new Promise (<anonymous>)
    at mapper (/var/lib/jenkins/workspace/elastic+kibana+pipeline-pull-request/kibana/node_modules/jest-jasmine2/build/queueRunner.js:28:19)
    at /var/lib/jenkins/workspace/elastic+kibana+pipeline-pull-request/kibana/node_modules/jest-jasmine2/build/queueRunner.js:75:41
    at processTicksAndRejections (internal/process/task_queues.js:95:5)

---

Metrics [docs]

Page load bundle

Size of the bundles that are downloaded on every page load. Target size is below 100kb

id	before	after	diff
data	837.7KB	838.0KB	+308.0B

To update your PR or re-run it, just comment with:
@elasticmachine merge upstream

[tsullivan]

Hi @ppisljar should this be in Draft status?