refactor(licensing): replace Pro branding with Community/Skipper/Admiral tiers (#375)

Eliminate all references to "Pro" across backend, frontend, and docs.
Internal tier value renamed from 'pro' to 'paid'; user-facing text now
uses the thematic tier names (Community, Skipper, Admiral).

- Rename LicenseTier 'pro' to 'paid' in backend and frontend types
- Rename requirePro guard to requirePaid, error code PRO_REQUIRED to PAID_REQUIRED
- Rename ProGate.tsx to PaidGate.tsx with updated copy
- Fix: trial users can now see upgrade/purchase cards in Settings
- Update all docs and openapi.yaml to use correct tier names

backend/src/__tests__/auth.test.ts

@@ -99,7 +99,7 @@ describe('POST /api/system/console-token', () => {
   // Console-token requires Admiral tier — mock LicenseService for the happy-path test
   beforeAll(async () => {
     const { LicenseService } = await import('../services/LicenseService');
-    vi.spyOn(LicenseService.getInstance(), 'getTier').mockReturnValue('pro');
+    vi.spyOn(LicenseService.getInstance(), 'getTier').mockReturnValue('paid');
     vi.spyOn(LicenseService.getInstance(), 'getVariant').mockReturnValue('team');
   });