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/services/SchedulerService.ts

@@ -49,9 +49,9 @@ export class SchedulerService {
         this.isProcessing = true;
         try {
             const ls = LicenseService.getInstance();
-            const isPro = ls.getTier() === 'pro';
-            const isAdmiral = isPro && ls.getVariant() === 'team';
-            if (!isPro) return; // No scheduled tasks for non-Pro tiers
+            const isPaid = ls.getTier() === 'paid';
+            const isAdmiral = isPaid && ls.getVariant() === 'team';
+            if (!isPaid) return; // No scheduled tasks for unpaid tiers
 
             const db = DatabaseService.getInstance();
             const now = Date.now();