docs(api): synchronize API.md with actual routes in routes/mod.rs (#7)

[ghzhost]

Summary

Closes #7.

Synchronizes with the live router registered in :

• Updated Base URL notation to standard service base URL ( / ).
• Documented authentication requirements across all protected and public endpoints.
• Added standard success and error response envelope structure.
• Documented all registered routes:
  • Health ()
  • Authentication (, )
  • Payments (, , , )
  • Transactions (, )
  • Accounts (, )
  • Rates ()
  • Subscriptions (, , , )
  • Payment Requests (, , , , )
  • Escrows (, , , , , , )
  • Keeper ()
• Removed obsolete and unregistered stub endpoints (, etc.) that are not present in the live router.