docs: Add spec for billing feature

[Rockyy174]

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[sourcery-ai]

Hey - I've left some high level feedback:

• Consider adding explicit handling for invalid or unknown plan / billing_period values (both on the billing-intent route and in backend APIs), including what the UX fallback should be so website or URL mistakes don’t break the flow.
• It may be useful to spell out how conflicting updates are resolved when both an owner-triggered billing/refresh and a webhook-driven CustomerStateSync occur close together, to avoid ambiguous final state or unnecessary retries.

Prompt for AI Agents

Please address the comments from this code review:

## Overall Comments
- Consider adding explicit handling for invalid or unknown `plan` / `billing_period` values (both on the billing-intent route and in backend APIs), including what the UX fallback should be so website or URL mistakes don’t break the flow.
- It may be useful to spell out how conflicting updates are resolved when both an owner-triggered `billing/refresh` and a webhook-driven `CustomerStateSync` occur close together, to avoid ambiguous final state or unnecessary retries.

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