## Why
PR #20559 added opt-in strict config parsing to the config-loading
command surfaces, but `codex exec-server` was left out. That meant
`codex exec-server --strict-config` was rejected even though the command
can load config for remote registration, and local server startup had no
way to fail fast on misspelled config keys.
## What Changed
- Added `--strict-config` to `codex exec-server`.
- Allowed root-level inheritance from `codex --strict-config
exec-server`.
- Validated config before local exec-server startup when strict mode is
requested.
- Reused the loaded strict-config-aware config for remote exec-server
registration auth.
- Added CLI coverage showing `codex exec-server --strict-config` rejects
unknown config fields.
## Verification
- `cargo test -p codex-cli`
- New integration test:
`strict_config_rejects_unknown_config_fields_for_exec_server`
## Documentation
Any strict-config command list on developers.openai.com/codex should
include `codex exec-server` with the other supported config-loading
entry points.
