chore(backend): add integration test for end-to-end invoice generation

[MerlinTheWhiz]

Closes #230

Changes made:

• Added integration test for e2e invoice generation

Summarized test output:

Tests:       26 passed, 26 total
Snapshots:   0 total
Time:        4.502 s
Ran all test suites matching tests/integration/billing.test.ts.

Security and pr note:

• PR_BILLING_INVOICE_E2E_NOTES.md
• SECURITY_AND_DATA_INTEGRITY_NOTES.md

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@MerlinTheWhiz Great news! 🎉 Based on an automated assessment of this PR, the linked Wave issue(s) no longer count against your application limits.

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