* fix(studio): harden system prompt persistence and storage fallback
* Exclude checkpoint from localStorage persistence for PR #4538
checkpoint is backend-owned state -- refresh() already syncs it from
getInferenceStatus() on every page load. Persisting it to localStorage
causes a stale model ID to survive across backend restarts, which
prevents auto-load from triggering when no model is actually loaded.
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Co-authored-by: Daniel Han <danielhanchen@gmail.com>