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

frontend/src/components/settings/DeveloperSection.tsx

@@ -34,7 +34,7 @@ function SettingsSkeleton() {
 }
 
 export function DeveloperSection({ settings, onSettingChange, onSave, isSaving, isLoading, isRemote }: DeveloperSectionProps) {
-    const { isPro, license } = useLicense();
+    const { isPaid, license } = useLicense();
 
     return (
         <div className="space-y-6">
@@ -143,7 +143,7 @@ export function DeveloperSection({ settings, onSettingChange, onSave, isSaving,
                                 </div>
                             </div>
 
-                            {isPro && license?.variant === 'team' && (
+                            {isPaid && license?.variant === 'team' && (
                                 <div className="flex items-center justify-between gap-4 pt-4 border-t border-glass-border">
                                     <div className="space-y-0.5">
                                         <Label className="text-base">Audit Log Retention</Label>