[8.x] Consume elasticsearch.publicBaseUrl where possible (#192741) (#…

…193838)

# Backport

This will backport the following commits from `main` to `8.x`:
- [Consume elasticsearch.publicBaseUrl where possible
(#192741)](#192741)

<!--- Backport version: 8.9.8 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sqren/backport)

<!--BACKPORT [{"author":{"name":"Sander
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elasticsearch.publicBaseUrl where possible (#192741)\n\n##
Summary\r\n\r\nThis actually consumes the public base url in the cloud
plugin and the\r\nplaces depending on the `elasticsearchUrl` value
populated there.\r\n\r\n---------\r\n\r\nCo-authored-by: Rodney Norris
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elasticsearch.publicBaseUrl where possible (#192741)\n\n##
Summary\r\n\r\nThis actually consumes the public base url in the cloud
plugin and the\r\nplaces depending on the `elasticsearchUrl` value
populated there.\r\n\r\n---------\r\n\r\nCo-authored-by: Rodney Norris
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elasticsearch.publicBaseUrl where possible (#192741)\n\n##
Summary\r\n\r\nThis actually consumes the public base url in the cloud
plugin and the\r\nplaces depending on the `elasticsearchUrl` value
populated there.\r\n\r\n---------\r\n\r\nCo-authored-by: Rodney Norris
<rodney@tattdcodemonkey.com>","sha":"b4a7b2e2164974e5dd9b8c1708c35d58bd021105"}},{"branch":"8.x","label":"v8.16.0","labelRegex":"^v8.16.0$","isSourceBranch":false,"url":"https://github.com/elastic/kibana/pull/193442","number":193442,"state":"OPEN"}]}]
BACKPORT-->