refactor(server): partner search dto (#10902)

* refactor(server): partner search dto

* fix: missed reference

* mobile fix

---------

Co-authored-by: Alex Tran <alex.tran1502@gmail.com>

open-api/immich-openapi-specs.json

@@ -3660,11 +3660,7 @@
             "required": true,
             "in": "query",
             "schema": {
-              "enum": [
-                "shared-by",
-                "shared-with"
-              ],
-              "type": "string"
+              "$ref": "#/components/schemas/PartnerDirection"
             }
           }
         ],
@@ -9473,6 +9469,13 @@
         ],
         "type": "object"
       },
+      "PartnerDirection": {
+        "enum": [
+          "shared-by",
+          "shared-with"
+        ],
+        "type": "string"
+      },
       "PartnerResponseDto": {
         "properties": {
           "avatarColor": {