[DOCS] Fixed edit links for ILM APIs and added the APIs to the REST ref (#35070)

* [DOCS] Fixed edit links for ILM APIs and added the APIs to the REST API section.

* [DOCS] Fixed link to ILM APIs.

docs/reference/ilm/index.asciidoc

@@ -7,10 +7,10 @@
 :ILM:             Index lifecycle management
 [partintro]
 --
-The {ILM} APIs enable you to automate how you want to manage your indices over
-time. Rather than simply performing management actions on your indices on a set
-schedule, you can base actions on other factors such as shard
-size and performance requirements.
+The <<index-lifecycle-management-api, {ilm} APIs>> enable you to automate how you
+want to manage your indices over time. Rather than simply performing management
+actions on your indices on a set schedule, you can base actions on other factors
+such as shard size and performance requirements.
 
 You control how indices are handled as they age by attaching a
 lifecycle policy to the index template used to create them. You can update
@@ -49,23 +49,14 @@ hardware.
 . Delete the index once the required 30 day retention period is reached.
 --
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/getting-started-ilm.asciidoc
 include::getting-started-ilm.asciidoc[]
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/using-policies--rollover.asciidoc
 include::using-policies-rollover.asciidoc[]
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/set-up-policy.asciidoc
 include::set-up-lifecycle-policy.asciidoc[]
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/update-lifecycle-policy.asciidoc
 include::update-lifecycle-policy.asciidoc[]
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/get-index-lifecycle-information.asciidoc
 include::get-index-lifecycle-information.asciidoc[]
 
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/pause-resume-ilm.asciidoc
 include::start-stop-ilm.asciidoc[]
-
-:edit_url: https://github.com/elastic/elasticsearch/edit/{branch}/x-pack/docs/en/ilm/apis/ilm-api.asciidoc
-include::{es-repo-dir}/ilm/apis/ilm-api.asciidoc[]

docs/reference/rest-api/index.asciidoc

@@ -10,6 +10,7 @@ directly to configure and access {xpack} features.
 * <<info-api,Info API>>
 * <<ccr-apis,Cross-cluster replication APIs>>
 * <<graph-explore-api,Graph Explore API>>
+* <<index-lifecycle-management-api,Index lifecycle management APIs>>
 * <<licensing-apis,Licensing APIs>>
 * <<ml-apis,Machine Learning APIs>>
 * <<security-api,Security APIs>>
@@ -22,6 +23,7 @@ directly to configure and access {xpack} features.
 include::info.asciidoc[]
 include::{es-repo-dir}/ccr/apis/ccr-apis.asciidoc[]
 include::{es-repo-dir}/graph/explore.asciidoc[]
+include::{es-repo-dir}/ilm/apis/ilm-api.asciidoc[]
 include::{es-repo-dir}/licensing/index.asciidoc[]
 include::{es-repo-dir}/migration/migration.asciidoc[]
 include::{es-repo-dir}/ml/apis/ml-api.asciidoc[]