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.v2.schemas.json

@@ -3730,19 +3730,6 @@
             }
           ]
         },
-        "profile": {
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "profiles": {
-          "additionalProperties": {
-            "$ref": "#/definitions/ProfileV2"
-          },
-          "default": {},
-          "type": "object"
-        },
         "review_model": {
           "type": [
             "string",
@@ -9699,107 +9686,6 @@
       ],
       "type": "object"
     },
-    "ProfileV2": {
-      "additionalProperties": true,
-      "properties": {
-        "approval_policy": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/AskForApproval"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        },
-        "approvals_reviewer": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/ApprovalsReviewer"
-            },
-            {
-              "type": "null"
-            }
-          ],
-          "description": "[UNSTABLE] Optional profile-level override for where approval requests are routed for review. If omitted, the enclosing config default is used."
-        },
-        "chatgpt_base_url": {
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "model": {
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "model_provider": {
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "model_reasoning_effort": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/ReasoningEffort"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        },
-        "model_reasoning_summary": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/ReasoningSummary"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        },
-        "model_verbosity": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/Verbosity"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        },
-        "service_tier": {
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "tools": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/ToolsV2"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        },
-        "web_search": {
-          "anyOf": [
-            {
-              "$ref": "#/definitions/WebSearchMode"
-            },
-            {
-              "type": "null"
-            }
-          ]
-        }
-      },
-      "type": "object"
-    },
     "RateLimitReachedType": {
       "enum": [
         "rate_limit_reached",