Wire the Servers overview's Proxmox badge to the integration color setting

The new integration badge-color setting only reached the Integrations
page's Manage table — the Servers & Tasks overview card grid had its
own hardcoded bg-purple-lt badge for Proxmox-linked servers that never
picked it up. Reuses the same typeBadgeStyle pattern already used
there and in the DNS module.

Note: until a Proxmox color is set in Settings -> Badges, this badge
now renders with Tabler's default neutral badge style rather than
purple, matching how every other badge customized this way already
behaves before a color is chosen.

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

web/src/pages/ServersTasks.tsx

@@ -1,4 +1,4 @@
-import { useCallback, useEffect, useMemo, useState } from "react";
+import { useCallback, useEffect, useMemo, useState, type CSSProperties } from "react";
 import { Link } from "react-router-dom";
 import {
   api,
@@ -22,6 +22,12 @@ const SCHEDULE_TYPE_OPTIONS: { value: ScheduleType; label: string }[] = [
   { value: "manual", label: "Other / manual" },
 ];
 
+function typeBadgeStyle(colors: Record<string, string>, type: string): CSSProperties {
+  const color = colors[type];
+  if (!color) return {};
+  return { backgroundColor: `${color}22`, color, border: `1px solid ${color}55` };
+}
+
 function installCommand(token: string, insecure: boolean): string {
   const curlFlags = insecure ? "-fsSL -k" : "-fsSL";
   const envVars = insecure
@@ -51,6 +57,11 @@ export default function ServersTasks({ user }: { user: CurrentUser }) {
   const [tasks, setTasks] = useState<TaskRecord[] | null>(null);
   const [error, setError] = useState<string | null>(null);
   const [managingServers, setManagingServers] = useState(false);
+  const [integrationColors, setIntegrationColors] = useState<Record<string, string>>({});
+
+  useEffect(() => {
+    api.settings.integrationColors().then((res) => setIntegrationColors(res.integrationColors)).catch(() => {});
+  }, []);
 
   const [filters, setFilters] = useState({
     serverId: undefined as number | undefined,
@@ -381,7 +392,9 @@ export default function ServersTasks({ user }: { user: CurrentUser }) {
                           <div className="text-secondary small">{s.hostname ?? "no hostname reported"}</div>
                         </div>
                         {s.proxmoxIntegrationId ? (
-                          <span className="badge bg-purple-lt text-purple">Proxmox</span>
+                          <span className="badge" style={typeBadgeStyle(integrationColors, "proxmox")}>
+                            Proxmox
+                          </span>
                         ) : s.lastSeenAt ? (
                           <span className="badge bg-green-lt text-green">Agent</span>
                         ) : (