Index prefixes for searchable snapshots (#78474)

* Index prefixes for searchable snapshots

added a note about how ILM managed indices are prefixed with "restored-" or "partial-" when they are either fully or partially mounted for searchable snapshots

* Apply suggestions from code review

Co-authored-by: debadair <debadair@elastic.co>

docs/reference/searchable-snapshots/index.asciidoc

@@ -132,6 +132,8 @@ slower than with a regular index because a search may need some data that has
 not yet been retrieved into the local copy. If that happens, {es} will eagerly
 retrieve the data needed to complete the search in parallel with the ongoing
 recovery.
++
+Indices managed by {ilm-init} are prefixed with `recovered-` when fully mounted.
 
 [[partially-mounted]]
 Partially mounted index::
@@ -150,6 +152,8 @@ partially mounted index still returns search results quickly, even for
 large data sets, because the layout of data in the repository is heavily
 optimized for search. Many searches will need to retrieve only a small subset of
 the total shard data before returning results.
++
+Indices managed by {ilm-init} are prefixed with `partial-` when partially mounted.
 
 To partially mount an index, you must have one or more nodes with a shared cache
 available. By default, dedicated frozen data tier nodes (nodes with the