[Playground][Backend] Saving Playground CRUD (#217761)

## Summary

This PR creates CRUD endpoints for search playgrounds. This will enable
us to make new pages for saved playgrounds that are shared in a space.

## Notes 

Usages of `ALL_SAVED_OBJECT_INDICES` had to be updated to include
`ignore_unavailable` since a new index was added for search solution
saved objects, but these are not always registered when search plugins
are disabled. Because of this refresh and other calls using
`ALL_SAVED_OBJECT_INDICES` were failing when the new
`.kibana_search_solution` index did not exist.

### Checklist

- [x] Any text added follows [EUI's writing
guidelines](https://elastic.github.io/eui/#/guidelines/writing), uses
sentence case text and includes [i18n
support](https://github.com/elastic/kibana/blob/main/src/platform/packages/shared/kbn-i18n/README.md)
- [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

---------

Co-authored-by: kibanamachine <42973632+kibanamachine@users.noreply.github.com>
Co-authored-by: Gerard Soldevila <gerard.soldevila@elastic.co>
Co-authored-by: Elastic Machine <elasticmachine@users.noreply.github.com>

packages/kbn-check-mappings-update-cli/current_fields.json

@@ -927,6 +927,9 @@
     "username"
   ],
   "search-telemetry": [],
+  "search_playground": [
+    "name"
+  ],
   "security-ai-prompt": [
     "description",
     "model",

packages/kbn-check-mappings-update-cli/current_mappings.json

@@ -3069,6 +3069,19 @@
     "dynamic": false,
     "properties": {}
   },
+  "search_playground": {
+    "dynamic": false,
+    "properties": {
+      "name": {
+        "fields": {
+          "keyword": {
+            "type": "keyword"
+          }
+        },
+        "type": "text"
+      }
+    }
+  },
   "security-ai-prompt": {
     "dynamic": false,
     "properties": {