feat(web): add badge API route

Add GET endpoint for badge SVG generation with hex color validation,
text length limit, and cache-control headers.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: wontory

apps/web/app/api/badge/route.ts

@@ -0,0 +1,38 @@
+import { generateBadgeSvg } from '@tech-stack/badge'
+import type { NextRequest } from 'next/server'
+import { resolveSimpleIcon } from '#utils/simple-icon'
+
+const HEX_COLOR = /^[0-9a-fA-F]{3,8}$/
+
+export async function GET(request: NextRequest) {
+  const { searchParams } = request.nextUrl
+  const slug = searchParams.get('slug') || ''
+  const text = (searchParams.get('text') || '').slice(0, 100)
+  const highlight = searchParams.get('highlight') === 'true'
+  const rawTextColor = searchParams.get('textColor') || ''
+  const rawIconColor = searchParams.get('iconColor') || ''
+  const rawBgColor = searchParams.get('bgColor') || ''
+  const textColor = HEX_COLOR.test(rawTextColor) ? rawTextColor : ''
+  const iconColor = HEX_COLOR.test(rawIconColor) ? rawIconColor : ''
+  const bgColor = HEX_COLOR.test(rawBgColor) ? rawBgColor : ''
+
+  const icon = slug ? resolveSimpleIcon(slug) : undefined
+
+  if (slug && !icon) {
+    return Response.json(
+      { error: `Icon with slug "${slug}" not found` },
+      { status: 404 },
+    )
+  }
+
+  const badgeSvg = generateBadgeSvg(
+    { slug, text, highlight, textColor, iconColor, bgColor },
+    icon ?? null,
+  )
+  return new Response(badgeSvg, {
+    headers: {
+      'content-type': 'image/svg+xml',
+      'cache-control': 'public, max-age=3600, s-maxage=3600',
+    },
+  })
+}