app-server: drop legacy profile config surface (#24067)

## Why

Legacy `[profiles.<name>]` config tables and the legacy `profile`
selector are being retired in favor of profile files selected with
`--profile <name>`. After #23886 removed the CLI-side legacy profile
plumbing, the app-server config surface still exposed those fields and
still carried conversion code for the old protocol shape.

## What changed

- Remove `profile`, `profiles`, and `ProfileV2` from the app-server
config protocol/schema output so `config/read` no longer returns legacy
profile config.
- Drop the old v1 `UserSavedConfig` profile conversion path from
`config`.
- Reject new app-server config writes under `profiles.*` with the same
migration direction used for `profile`, while still allowing callers to
clear existing legacy profile tables.
- Refresh app-server config coverage and the experimental API README
example around the remaining `Config` nesting path.

## Verification

- Added config-manager coverage that `config/read` omits legacy profile
config, `profiles.*` writes are rejected, and existing legacy profile
tables can still be cleared.
- Updated the v2 config RPC test to cover the rejected `profiles.*`
batch-write path.

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

@@ -7361,19 +7361,6 @@
               }
             ]
           },
-          "profile": {
-            "type": [
-              "string",
-              "null"
-            ]
-          },
-          "profiles": {
-            "additionalProperties": {
-              "$ref": "#/definitions/v2/ProfileV2"
-            },
-            "default": {},
-            "type": "object"
-          },
           "review_model": {
             "type": [
               "string",
@@ -13170,107 +13157,6 @@
         ],
         "type": "object"
       },
-      "ProfileV2": {
-        "additionalProperties": true,
-        "properties": {
-          "approval_policy": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/AskForApproval"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          },
-          "approvals_reviewer": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/ApprovalsReviewer"
-              },
-              {
-                "type": "null"
-              }
-            ],
-            "description": "[UNSTABLE] Optional profile-level override for where approval requests are routed for review. If omitted, the enclosing config default is used."
-          },
-          "chatgpt_base_url": {
-            "type": [
-              "string",
-              "null"
-            ]
-          },
-          "model": {
-            "type": [
-              "string",
-              "null"
-            ]
-          },
-          "model_provider": {
-            "type": [
-              "string",
-              "null"
-            ]
-          },
-          "model_reasoning_effort": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/ReasoningEffort"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          },
-          "model_reasoning_summary": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/ReasoningSummary"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          },
-          "model_verbosity": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/Verbosity"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          },
-          "service_tier": {
-            "type": [
-              "string",
-              "null"
-            ]
-          },
-          "tools": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/ToolsV2"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          },
-          "web_search": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/v2/WebSearchMode"
-              },
-              {
-                "type": "null"
-              }
-            ]
-          }
-        },
-        "type": "object"
-      },
       "RateLimitReachedType": {
         "enum": [
           "rate_limit_reached",