The v10 model cache never persists request headers (#5780). The registry's
startup cache readers (#loadCachedStandardProviderModels /
#loadCachedDiscoverableModels) read cache.models directly, so cached rows
replaced bundled models (github-copilot, kimi-code, nanogpt) with header-less
copies for the cache TTL after every restart. Restore bundled static headers,
drop unrestorable rows so bundled fallbacks win the merge, and mark
discoverable providers stale when header-bearing models were excluded.
refreshProvider's #reloadStaticModels could also evict models discovered by
other runtime providers; re-merge them from cache with online-if-uncached.