[DOCS] Clarify Update API does not replace fields with sparse_vector field (elastic#135788)

* [DOCS] Clarify Update API does not replace fields with sparse_vector field

Updated the documentation for `sparse_vector` fields to clarify merging behavior, replacement methods, and limitations.

🚗 Compiled all the admonitions into a limitations section

* Fix links

* Fix rank link to rank_features

* idem

* Fix formatting and wording

* Add applies_to and products metadata

Author: leemthompo

docs/reference/elasticsearch/mapping-reference/sparse-vector.md

@@ -1,4 +1,9 @@
 ---
+applies_to:
+  stack:
+  serverless:
+products:
+  - id: elasticsearch
 navigation_title: "Sparse vector"
 mapped_pages:
   - https://www.elastic.co/guide/en/elasticsearch/reference/current/sparse-vector.html
@@ -150,24 +155,81 @@ GET my-index-000001/_search
 }
 ```
 
-::::{note}
-`sparse_vector` fields can not be included in indices that were **created** on {{es}} versions between 8.0 and 8.10
-::::
+## Updating `sparse_vector` fields
 
+When using the [Update API](https://www.elastic.co/docs/api/doc/elasticsearch/operation/operation-update) with the `doc` parameter, `sparse_vector` fields behave like nested objects and are **merged** rather than replaced. This means:
 
-::::{note}
-`sparse_vector` fields only support strictly positive values. Negative values will be rejected.
-::::
+- Existing tokens in the sparse vector are preserved
+- New tokens are added
+- Tokens present in both the existing and new data will have their values updated
 
+This is different from primitive array fields (like `keyword`), which are replaced entirely during updates.
 
-::::{note}
-`sparse_vector` fields do not support [analyzers](docs-content://manage-data/data-store/text-analysis.md), querying, sorting or aggregating. They may only be used within specialized queries. The recommended query to use on these fields are [`sparse_vector`](/reference/query-languages/query-dsl/query-dsl-sparse-vector-query.md) queries. They may also be used within legacy [`text_expansion`](/reference/query-languages/query-dsl/query-dsl-text-expansion-query.md) queries.
-::::
+### Example of merging behavior
 
+Original document:
 
-::::{note}
-`sparse_vector` fields only preserve 9 significant bits for the precision, which translates to a relative error of about 0.4%.
-::::
+```console
+PUT /my-index/_doc/1
+{
+  "my_vector": {
+    "token_a": 0.5,
+    "token_b": 0.8
+  }
+}
+```
+
+Partial update:
+
+```console
+POST /my-index/_update/1
+{
+  "doc": {
+    "my_vector": {
+      "token_c": 0.3
+    }
+  }
+}
+```
+
+Observe that tokens are merged, not replaced:
+
+```json
+{
+  "my_vector": {
+    "token_a": 0.5,
+    "token_b": 0.8,
+    "token_c": 0.3
+  }
+}
+```
+
+### Replacing the entire `sparse_vector` field
+
+To replace the entire contents of a `sparse_vector` field, use a [script](docs-content://explore-analyze/scripting/modules-scripting-using.md) in your update request:
+
+```console
+POST /my-index/_update/1
+{
+  "script": {
+    "source": "ctx._source.my_vector = params.new_vector",
+    "params": {
+      "new_vector": {
+        "token_x": 1.0,
+        "token_y": 0.6
+      }
+    }
+  }
+}
+```
 
+:::{note}
+This same merging behavior also applies to [`rank_features` fields](/reference/elasticsearch/mapping-reference/rank-features.md), because they are also object-like structures.
+:::
 
+## Important notes and limitations
 
+- `sparse_vector` fields cannot be included in indices that were **created** on {{es}} versions between 8.0 and 8.10
+- `sparse_vector` fields only support strictly positive values. Negative values will be rejected.
+- `sparse_vector` fields do not support [analyzers](docs-content://manage-data/data-store/text-analysis.md), querying, sorting or aggregating. They may only be used within specialized queries. The recommended query to use on these fields are [`sparse_vector`](/reference/query-languages/query-dsl/query-dsl-sparse-vector-query.md) queries. They may also be used within legacy [`text_expansion`](/reference/query-languages/query-dsl/query-dsl-text-expansion-query.md) queries.
+- `sparse_vector` fields only preserve 9 significant bits for the precision, which translates to a relative error of about 0.4%.