refactor(api): convert bot accounts through the admin user edit endpoint (#39355)

Follow-up to https://github.com/go-gitea/gitea/pull/38966. Replaces the
unreleased `POST /admin/users/{username}/convert-type` endpoint with a
`type` field on `PATCH /admin/users/{username}`.

templates/swagger/v1-swagger.generated.json

@@ -1144,52 +1144,6 @@
         }
       }
     },
-    "/admin/users/{username}/convert-type": {
-      "post": {
-        "consumes": [
-          "application/json"
-        ],
-        "produces": [
-          "application/json"
-        ],
-        "tags": [
-          "admin"
-        ],
-        "summary": "Convert an account between the user and bot types",
-        "operationId": "adminConvertUserType",
-        "parameters": [
-          {
-            "type": "string",
-            "description": "username of the user to convert",
-            "name": "username",
-            "in": "path",
-            "required": true
-          },
-          {
-            "name": "body",
-            "in": "body",
-            "required": true,
-            "schema": {
-              "$ref": "#/definitions/ConvertUserTypeOption"
-            }
-          }
-        ],
-        "responses": {
-          "204": {
-            "$ref": "#/responses/empty"
-          },
-          "400": {
-            "$ref": "#/responses/error"
-          },
-          "403": {
-            "$ref": "#/responses/forbidden"
-          },
-          "404": {
-            "$ref": "#/responses/notFound"
-          }
-        }
-      }
-    },
     "/admin/users/{username}/keys": {
       "post": {
         "consumes": [
@@ -26790,25 +26744,6 @@
       },
       "x-go-package": "gitea.dev/modules/structs"
     },
-    "ConvertUserTypeOption": {
-      "description": "ConvertUserTypeOption options when converting a user between individual and bot",
-      "type": "object",
-      "required": [
-        "user_type"
-      ],
-      "properties": {
-        "user_type": {
-          "description": "The target user type",
-          "type": "string",
-          "enum": [
-            "User",
-            "Bot"
-          ],
-          "x-go-name": "UserType"
-        }
-      },
-      "x-go-package": "gitea.dev/modules/structs"
-    },
     "CreateAccessTokenOption": {
       "description": "CreateAccessTokenOption options when create access token",
       "type": "object",
@@ -29457,6 +29392,17 @@
           "format": "int64",
           "x-go-name": "SourceID"
         },
+        "type": {
+          "description": "The user type",
+          "type": "string",
+          "enum": [
+            "User",
+            "Organization",
+            "Bot"
+          ],
+          "x-go-enum-desc": "User UserTypeStringUser\nOrganization UserTypeStringOrganization\nBot UserTypeStringBot",
+          "x-go-name": "Type"
+        },
         "visibility": {
           "description": "User visibility level: public, limited, or private",
           "type": "string",
@@ -33820,7 +33766,7 @@
           "x-go-name": "StarredRepos"
         },
         "type": {
-          "description": "the account type",
+          "description": "the user type",
           "type": "string",
           "enum": [
             "User",