fix: Avoid full page reload on billing catalog sync and updates

[Rockyy174]

No description provided.

[sourcery-ai]

Hey - I've left some high level feedback:

• The new syncBillingCatalogProducts, archiveBillingCatalogProduct, and setActiveBillingCatalogProduct helpers are exported from the main page module purely to support tests; consider moving them into a small internal helper module (or keeping them unexported and testing via component behavior) to avoid widening the public surface of index.tsx.

Prompt for AI Agents

Please address the comments from this code review:

## Overall Comments
- The new `syncBillingCatalogProducts`, `archiveBillingCatalogProduct`, and `setActiveBillingCatalogProduct` helpers are exported from the main page module purely to support tests; consider moving them into a small internal helper module (or keeping them unexported and testing via component behavior) to avoid widening the public surface of `index.tsx`.

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