Extend badge color settings to cover integration types too

Settings → DNS Badges only let you customize DNS provider badge
colors. Expand it into a general Badges page with a second section
for the six integration types (Tailscale, Proxmox, Synology,
Semaphore, Gitea, Dockhand), applied to the type badge in the Manage
integrations table.

- New integrationColors key on AppSettings, stored/merged the same way
  as providerColors via the existing settingsStore.
- New GET /api/settings/integration-colors — non-secret, any signed-in
  user, mirroring /provider-colors — so the badge color can be read
  without needing admin access to the full settings payload.
- Renamed DnsBadgeSettings.tsx -> BadgeSettings.tsx (route
  /settings/dns-badges -> /settings/badges, sub-nav label "DNS
  Badges" -> "Badges") with both color sections saved together.

Verified end-to-end against the real dev server: PUT persists
integration colors independently of provider colors, the public
integration-colors endpoint reflects updates immediately, and the
change is audit-logged.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

server/src/services/settingsStore.ts

@@ -44,6 +44,7 @@ export interface NotificationEvents {
 }
 
 export type ProviderColors = Record<string, string>;
+export type IntegrationColors = Record<string, string>;
 
 export interface AppSettings {
   gotify: GotifySettings;
@@ -52,6 +53,7 @@ export interface AppSettings {
   webhook: WebhookSettings;
   notifications: NotificationEvents;
   providerColors: ProviderColors;
+  integrationColors: IntegrationColors;
 }
 
 const DEFAULTS: AppSettings = {
@@ -68,6 +70,7 @@ const DEFAULTS: AppSettings = {
     timezone: "UTC",
   },
   providerColors: {},
+  integrationColors: {},
 };
 
 const KEYS = Object.keys(DEFAULTS) as (keyof AppSettings)[];