[codex] Add owner nudge app-server API (#18220)

## Summary

Second PR in the split from #17956. Stacked on #18227.

- adds app-server v2 protocol/schema support for
`account/sendAddCreditsNudgeEmail`
- adds the backend-client `send_add_credits_nudge_email` request and
request body mapping
- handles the app-server request with auth checks, backend call, and
cooldown mapping
- adds the disabled `workspace_owner_usage_nudge` feature flag and
focused app-server/backend tests

## Validation

- `cargo test -p codex-backend-client`
- `cargo test -p codex-app-server-protocol`
- `cargo test -p codex-app-server rate_limits`
- `cargo test -p codex-tui workspace_`
- `cargo test -p codex-tui status_`
- `just fmt`
- `just fix -p codex-backend-client`
- `just fix -p codex-app-server-protocol`
- `just fix -p codex-app-server`
- `just fix -p codex-tui`

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.schemas.json

@@ -1440,6 +1440,30 @@
           "title": "Account/rateLimits/readRequest",
           "type": "object"
         },
+        {
+          "properties": {
+            "id": {
+              "$ref": "#/definitions/v2/RequestId"
+            },
+            "method": {
+              "enum": [
+                "account/sendAddCreditsNudgeEmail"
+              ],
+              "title": "Account/sendAddCreditsNudgeEmailRequestMethod",
+              "type": "string"
+            },
+            "params": {
+              "$ref": "#/definitions/v2/SendAddCreditsNudgeEmailParams"
+            }
+          },
+          "required": [
+            "id",
+            "method",
+            "params"
+          ],
+          "title": "Account/sendAddCreditsNudgeEmailRequest",
+          "type": "object"
+        },
         {
           "properties": {
             "id": {
@@ -5103,6 +5127,20 @@
         "title": "AccountUpdatedNotification",
         "type": "object"
       },
+      "AddCreditsNudgeCreditType": {
+        "enum": [
+          "credits",
+          "usage_limit"
+        ],
+        "type": "string"
+      },
+      "AddCreditsNudgeEmailStatus": {
+        "enum": [
+          "sent",
+          "cooldown_active"
+        ],
+        "type": "string"
+      },
       "AgentMessageDeltaNotification": {
         "$schema": "http://json-schema.org/draft-07/schema#",
         "properties": {
@@ -12267,6 +12305,32 @@
         },
         "type": "object"
       },
+      "SendAddCreditsNudgeEmailParams": {
+        "$schema": "http://json-schema.org/draft-07/schema#",
+        "properties": {
+          "creditType": {
+            "$ref": "#/definitions/v2/AddCreditsNudgeCreditType"
+          }
+        },
+        "required": [
+          "creditType"
+        ],
+        "title": "SendAddCreditsNudgeEmailParams",
+        "type": "object"
+      },
+      "SendAddCreditsNudgeEmailResponse": {
+        "$schema": "http://json-schema.org/draft-07/schema#",
+        "properties": {
+          "status": {
+            "$ref": "#/definitions/v2/AddCreditsNudgeEmailStatus"
+          }
+        },
+        "required": [
+          "status"
+        ],
+        "title": "SendAddCreditsNudgeEmailResponse",
+        "type": "object"
+      },
       "ServerRequestResolvedNotification": {
         "$schema": "http://json-schema.org/draft-07/schema#",
         "properties": {