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/ServerNotification.json

@@ -6546,4 +6546,4 @@
     }
   ],
   "title": "ServerNotification"
-}
+}