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>

README.md

@@ -49,7 +49,8 @@ All modules from the original plan are built:
 - **Settings** (admin-only) — notification channels (Gotify, ntfy, SMTP,
   generic webhook) with per-channel test buttons, per-event toggles (DNS
   record added/updated/deleted, daily secret-expiry reminder with a
-  configurable time/timezone), and DNS provider badge-color customization.
+  configurable time/timezone), and badge-color customization for both DNS
+  providers and integration types.
 
 All six integrations follow the same config-in-UI + encrypted-credentials
 pattern, added (and edited — e.g. to rotate an expired API token without