[Synthetics] remove public SO usage from delete params flow

[dominiqueclarke]

Summary

Relates to #153399

Removes public SO client usage for the delete params workflow by directly calling the DELETE params api.

Addresses the following task from the related issue

• https://github.com/elastic/kibana/blob/main/x-pack/plugins/synthetics/public/apps/synthetics/components/settings/global_params/delete_param.tsx#L42

Testing

1. Navigate to Synthetics global params
2. Create a param
3. Delete that param
4. Create two more params
5. Using bulk actions, select both params and delete both params

[elasticmachine]

Pinging @elastic/uptime (Team:uptime)

[apmmachine]

🤖 GitHub comments

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Just comment with:

• /oblt-deploy : Deploy a Kibana instance using the Observability test environments.
• run elasticsearch-ci/docs : Re-trigger the docs validation. (use unformatted text in the comment!)

[kibana-ci]

💚 Build Succeeded

• Buildkite Build
• Commit: 7012443

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
synthetics	1.2MB	1.2MB	+73.0B

Unknown metric groups

ESLint disabled line counts

id	before	after	diff
enterpriseSearch	19	21	+2
securitySolution	400	404	+4
total			+6

References to deprecated APIs

id	before	after	diff
synthetics	115	114	-1

Total ESLint disabled count

id	before	after	diff
enterpriseSearch	20	22	+2
securitySolution	480	484	+4
total			+6

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

[shahzad31]

LGTM !!