[Watcher] Remove deprecated savedObjectsClient

[yuliacech]

Summary

Fixes #154035

This PR removes the saved objects client from the client-side code of the Watcher plugin. It seems not to be used anywhere so the removal should not cause any changes to the UI.
To test this PR, it should be enough to create/update/delete a couple of simple and advanced watches.

[elasticmachine]

Pinging @elastic/platform-deployment-management (Team:Deployment Management)

[kibana-ci]

💚 Build Succeeded

• Buildkite Build
• Commit: bae2bb5

Metrics [docs]

Async chunks

Total size of all lazy-loaded chunks that will be downloaded as the user navigates the app

id	before	after	diff
watcher	273.6KB	273.6KB	-33.0B

Page load bundle

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

id	before	after	diff
watcher	13.5KB	13.4KB	-37.0B

Unknown metric groups

ESLint disabled line counts

id	before	after	diff
securitySolution	433	436	+3

References to deprecated APIs

id	before	after	diff
watcher	8	2	-6

Total ESLint disabled count

id	before	after	diff
securitySolution	513	516	+3

History

• 💚 Build #118241 succeeded 37c19e8
• 💛 Build #117129 was flaky e7d2e49

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

[sabarasaba]

Thanks for patching this up @yuliacech! Changes lgtm, tested locally 🚀