Add JSON response format to entropy endpoints (#2673)

* Add JSON response format to entropy endpoints

Add account settings JSON endpoint returning account info including auto_postpone_period. Add auto_postpone_period to board JSON responses. Add JSON update support to both account and board entropy controllers.

* Add auto_postpone_period to all board response examples in API docs

* Use auto_postpone_period_in_days in JSON responses and API docs

* Use valid period values in permission tests

docs/API.md

@@ -434,6 +434,7 @@ __Response:__
     "name": "Fizzy",
     "all_access": true,
     "created_at": "2025-12-05T19:36:35.534Z",
+    "auto_postpone_period_in_days": 30,
     "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
     "creator": {
       "id": "03f5v9zjw7pz8717a4no1h8a7",
@@ -460,6 +461,7 @@ __Response:__
   "name": "Fizzy",
   "all_access": true,
   "created_at": "2025-12-05T19:36:35.534Z",
+  "auto_postpone_period_in_days": 30,
   "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
   "creator": {
     "id": "03f5v9zjw7pz8717a4no1h8a7",
@@ -484,7 +486,7 @@ Creates a new Board in the account.
 |-----------|------|----------|-------------|
 | `name` | string | Yes | The name of the board |
 | `all_access` | boolean | No | Whether any user in the account can access this board. Defaults to `true` |
-| `auto_postpone_period` | integer | No | Number of days of inactivity before cards are automatically postponed |
+| `auto_postpone_period_in_days` | integer | No | Number of days of inactivity before cards are automatically postponed (e.g. `30`) |
 | `public_description` | string | No | Rich text description shown on the public board page |
 
 __Request:__
@@ -514,7 +516,7 @@ Updates a Board. Only board administrators can update a board.
 |-----------|------|----------|-------------|
 | `name` | string | No | The name of the board |
 | `all_access` | boolean | No | Whether any user in the account can access this board |
-| `auto_postpone_period` | integer | No | Number of days of inactivity before cards are automatically postponed |
+| `auto_postpone_period_in_days` | integer | No | Number of days of inactivity before cards are automatically postponed (e.g. `30`) |
 | `public_description` | string | No | Rich text description shown on the public board page |
 | `user_ids` | array | No | Array of *all* user IDs who should have access to this board (only applicable when `all_access` is `false`) |
 
@@ -524,7 +526,7 @@ __Request:__
 {
   "board": {
     "name": "Updated board name",
-    "auto_postpone_period": 14,
+    "auto_postpone_period_in_days": 30,
     "public_description": "This is a **public** description of the board.",
     "all_access": false,
     "user_ids": [
@@ -567,6 +569,7 @@ HTTP/1.1 201 Created
   "name": "Fizzy",
   "all_access": true,
   "created_at": "2025-12-05T19:36:35.534Z",
+  "auto_postpone_period_in_days": 30,
   "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
   "creator": {
     "id": "03f5v9zjw7pz8717a4no1h8a7",
@@ -591,6 +594,72 @@ __Response:__
 
 Returns `204 No Content` on success.
 
+## Account
+
+### `GET /account/settings`
+
+Returns the current account.
+
+__Response:__
+
+```json
+{
+  "id": "03f5v9zjvypwh0t0e2rfh0h7k",
+  "name": "37signals",
+  "cards_count": 5,
+  "created_at": "2025-12-05T19:36:35.401Z",
+  "auto_postpone_period_in_days": 30
+}
+```
+
+The `auto_postpone_period_in_days` is the account-level default in days (e.g. `30`). Cards are automatically moved to "Not Now" after this period of inactivity. Each board can override this with its own value.
+
+### `PUT /account/entropy`
+
+Updates the account-level default auto close period. Requires admin role.
+
+__Request:__
+
+```json
+{
+  "entropy": {
+    "auto_postpone_period_in_days": 30
+  }
+}
+```
+
+__Response:__
+
+Returns the account object:
+
+```json
+{
+  "id": "03f5v9zjvypwh0t0e2rfh0h7k",
+  "name": "37signals",
+  "cards_count": 5,
+  "created_at": "2025-12-05T19:36:35.401Z",
+  "auto_postpone_period_in_days": 30
+}
+```
+
+### `PUT /:account_slug/boards/:board_id/entropy`
+
+Updates the auto close period for a specific board. Requires board admin permission.
+
+__Request:__
+
+```json
+{
+  "board": {
+    "auto_postpone_period_in_days": 90
+  }
+}
+```
+
+__Response:__
+
+Returns the board object.
+
 ## Webhooks
 
 Webhooks notify another application when something happens on a board. Only account admins can list, view, create, update, delete, or reactivate webhooks.
@@ -757,6 +826,7 @@ __Response:__
       "name": "Fizzy",
       "all_access": true,
       "created_at": "2025-12-05T19:36:35.534Z",
+      "auto_postpone_period_in_days": 30,
       "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
       "creator": {
         "id": "03f5v9zjw7pz8717a4no1h8a7",
@@ -810,6 +880,7 @@ __Response:__
     "name": "Fizzy",
     "all_access": true,
     "created_at": "2025-12-05T19:36:35.534Z",
+    "auto_postpone_period_in_days": 30,
     "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
     "creator": {
       "id": "03f5v9zjw7pz8717a4no1h8a7",
@@ -1077,6 +1148,7 @@ __Response:__
       "name": "Fizzy",
       "all_access": true,
       "created_at": "2025-12-05T19:36:35.534Z",
+      "auto_postpone_period_in_days": 30,
       "url": "http://fizzy.localhost:3006/897362094/boards/03f5v9zkft4hj9qq0lsn9ohcm",
       "creator": {
         "id": "03f5v9zjw7pz8717a4no1h8a7",