[Deprecations/Docs] Address uncommented apis (elastic#204198)

## Summary

elastic#203042 highlighted these APIs not having comments.

### Checklist

- [x]
[Documentation](https://www.elastic.co/guide/en/kibana/master/development-documentation.html)
was added for features that require explanation or tutorials

(cherry picked from commit 25b171d)

packages/core/deprecations/core-deprecations-server-internal/src/deprecations_service.ts

@@ -25,10 +25,14 @@ import { registerRoutes } from './routes';
 import { config as deprecationConfig, DeprecationConfigType } from './deprecation_config';
 import { registerApiDeprecationsInfo, registerConfigDeprecationsInfo } from './deprecations';
 
+/**
+ * Deprecation Service: Internal Start contract
+ */
 export interface InternalDeprecationsServiceStart {
   /**
    * Creates a {@link DeprecationsClient} with provided SO client and ES client.
-   *
+   * @param esClient Scoped Elasticsearch client
+   * @param savedObjectsClient Scoped SO Client
    */
   asScopedToClient(
     esClient: IScopedClusterClient,

packages/core/deprecations/core-deprecations-server/src/contracts.ts

@@ -87,27 +87,50 @@ import type { SavedObjectsClientContract } from '@kbn/core-saved-objects-api-ser
  * @public
  */
 export interface DeprecationsServiceSetup {
+  /**
+   * Registers deprecation messages or notices for a specific feature or functionality
+   * within the application. This allows developers to flag certain behaviors or APIs
+   * as deprecated, providing guidance and warnings for future deprecation plans.
+   *
+   * @param {RegisterDeprecationsConfig} deprecationContext - The configuration object containing
+   * information about the deprecated features, including messages, corrective actions,
+   * and any relevant metadata to inform users or developers about the deprecation.
+   */
   registerDeprecations: (deprecationContext: RegisterDeprecationsConfig) => void;
 }
 
 /**
+ * Options to provide when registering deprecations via {@link DeprecationsServiceSetup.registerDeprecations}.
  * @public
  */
 export interface RegisterDeprecationsConfig {
+  /**
+   * Method called when the user wants to list any existing deprecations.
+   * Returns the list of deprecation messages to warn about.
+   * @param {GetDeprecationsContext} context Scoped clients and helpers to ease fetching the deprecations.
+   */
   getDeprecations: (context: GetDeprecationsContext) => MaybePromise<DeprecationsDetails[]>;
 }
 
 /**
+ * Scoped clients and helpers to ease fetching the deprecations.
  * @public
  */
 export interface GetDeprecationsContext {
+  /** Elasticsearch client scoped to the current user */
   esClient: IScopedClusterClient;
+  /** Saved Objects client scoped to the current user and space */
   savedObjectsClient: SavedObjectsClientContract;
 }
 
 /**
+ * Provides a method to scope the {@link DeprecationsServiceSetup | Deprecations Service} to a specific domain.
  * @public
  */
 export interface DeprecationRegistryProvider {
+  /**
+   * Returns the {@link DeprecationsServiceSetup | Deprecations Service} scoped to a specific domain.
+   * @param domainId Domain ID to categorize the deprecations reported under it.
+   */
   getRegistry: (domainId: string) => DeprecationsServiceSetup;
 }

packages/core/deprecations/core-deprecations-server/src/request_handler_context.ts

@@ -15,6 +15,9 @@ import type { DomainDeprecationDetails } from '@kbn/core-deprecations-common';
  * @public
  */
 export interface DeprecationsClient {
+  /**
+   * Fetch all Kibana deprecations.
+   */
   getAllDeprecations: () => Promise<DomainDeprecationDetails[]>;
 }
 
@@ -23,5 +26,8 @@ export interface DeprecationsClient {
  * @public
  */
 export interface DeprecationsRequestHandlerContext {
+  /**
+   * {@link DeprecationsClient | Deprecations client} exposed in the request handler context.
+   */
   client: DeprecationsClient;
 }