Harden Codex takeover ownership signaling and serialize switch/takeover

Gate provider sync and switching on the restore backup / live placeholder
("is this live file owned by takeover?") instead of the lagging
proxy_config.enabled and proxy-running flags. The backup is created
before enabled=true is committed, so during that activation window the
old guards were blind and a concurrent sync/switch could rewrite the
taken-over live file, clearing Codex auth.json for a mis-categorized
provider.

Acquire a per-app switch lock around both set_takeover_for_app and
provider switching so the two cannot interleave, splitting the locking
entry points into outer (lock) / inner (no-lock) pairs to stay
deadlock-free. Preserve the official OAuth auth in provider-rebuilt
restore backups by routing the provider token into config.toml. Refine
takeover idempotency to require the live config to point at the current
proxy URL, rebuilding from backup when it does not.

Add unit and integration tests covering the official -> DeepSeek ->
takeover on/off lifecycle and the stopped-proxy switch path.